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Articles 1 - 24 of 24
Full-Text Articles in Algebra
Representations Of The Temperley-Lieb Algebra, Anne Moore
Representations Of The Temperley-Lieb Algebra, Anne Moore
Mathematics, Statistics, and Computer Science Honors Projects
This paper gives an introduction to Temperley-Lieb algebra that is easily accessible to undergraduates, presenting TL diagrams, the method for multiplying the diagrams, and the properties of the multiplication that it is necessary to preserve in a representation. The paper also gives a method for finding representations of the TL monoids (sets of diagrams classified by number of vertices) using Young tableaux, and shows that these representations are all of the irreducible representations. While ideas of Hecke algebra imply the fact that this method produces representations, this paper provides a direct proof, strictly within the field of representation theory. It …
Writing Representations Over Proper Division Subrings, Stephen P. Glasby
Writing Representations Over Proper Division Subrings, Stephen P. Glasby
All Faculty Scholarship for the College of the Sciences
Let �� be a division ring, and G a finite group of automorphisms of E whose elements are distinct modulo inner automorphisms of ��. Let �� = ��G be the division subring of elements of �� fixed by G. Given a representation p : �� →��d×d of an �� -algebra ��, we give necessary and sufficient conditions for p to be writable over ��. (Here ��d×d denotes the algebra of d×d matrices over ��, and a matrix A writes p over �� if A−1p(��)A ⊆ Fd×d.) We give an algorithm for constructing an …
A Classification Of Certain Maximal Subgroups Of Alternating Groups, Bret Benesh
A Classification Of Certain Maximal Subgroups Of Alternating Groups, Bret Benesh
Mathematics Faculty Publications
This paper addresses and extension of Problem 12.82 of the Kourovka notebook, which asks for all ordered pairs (n,m) such that the symmetric groups Sn embeds in Sm as a maximal subgroup. Problem 12.82 was answered in a previous paper by the author and Benjamin Newton. In this paper, we will consider the extension problem where we allow either or both of the groups from the ordered pair to be an alternating group.
Truncated Toeplitz Operators On Finite Dimensional Spaces, William T. Ross, Joseph A. Cima, Warren R. Wogen
Truncated Toeplitz Operators On Finite Dimensional Spaces, William T. Ross, Joseph A. Cima, Warren R. Wogen
Department of Math & Statistics Faculty Publications
In this paper, we study the matrix representations of compressions of Toeplitz operators to the finite dimensional model spaces H2ƟBH2, where B is a finite Blaschke product. In particular, we determine necessary and sufficient conditions - in terms of the matrix representation - of when a linear transformation on H2ƟBH2 is the compression of a Toeplitz operator. This result complements a related result of Sarason [6].
Indestructible Blaschke Products, William T. Ross
Indestructible Blaschke Products, William T. Ross
Department of Math & Statistics Faculty Publications
No abstract provided.
Review: Lie Structure In Semiprime Superalgebras With Superinvolution, Gizem Karaali
Review: Lie Structure In Semiprime Superalgebras With Superinvolution, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
On The Reproducing Kernel Hilbert Spaces Associated With The Fractional And Bi-Fractional Brownian Motions, Daniel Alpay, David Levanony
On The Reproducing Kernel Hilbert Spaces Associated With The Fractional And Bi-Fractional Brownian Motions, Daniel Alpay, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define a new function of two complex variables, which is a natural generalization of the classical Gamma function for the setting we consider.
Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan
Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan
Engineering Faculty Articles and Research
Following earlier work, a modal logic for T-coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yields an equational logic for the presheaf semantics of higher-order abstract syntax. As another application, we show how the move to functors between many-sorted varieties allows to modularly combine syntax and proof systems of different logics. Second, we show how to associate …
Students' Perceptions Of Sense Of Community In Abstract Algebra: Contributing Factors And Benefits, Hortensia Soto-Johnson, Nissa Yestness, Casey Dalton
Students' Perceptions Of Sense Of Community In Abstract Algebra: Contributing Factors And Benefits, Hortensia Soto-Johnson, Nissa Yestness, Casey Dalton
Mathematical Sciences Faculty Publications
In this phenomenological study, we explore how multiple assessments contribute to creating a sense of community (SOC) in an undergraduate abstract algebra course. Strike (2004) describes community as a process rather than a feeling and outlines four characteristics of community: coherence, cohesion, care, and contact. In this report, we describe contributing factors to and perceived benefits of SOC that students provided in an open-ended interview. Our findings indicate students viewed the teacher and the classroom environment as the primary sources of creating a SOC. Our findings also suggest students believed the SOC of the classroom increased classroom interaction and opened …
Review: Some Remarks On Quantized Lie Superalgebras Of Classical Type, Gizem Karaali
Review: Some Remarks On Quantized Lie Superalgebras Of Classical Type, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Degenerate Series Representations Of The Q-Deformed Algebra Soq′(R,S), Gizem Karaali
Review: Degenerate Series Representations Of The Q-Deformed Algebra Soq′(R,S), Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Iterated Aluthge Transforms: A Brief Survey, Jorge Antezana, Enrique R. Pujals, Demetrio Stojanoff
Iterated Aluthge Transforms: A Brief Survey, Jorge Antezana, Enrique R. Pujals, Demetrio Stojanoff
Publications and Research
Given an r × r complex matrix T, if T = U|T| is the polar decomposition of T, then the Aluthge transform is defined by
∆(T) = |T|1/2U|T|1/2.
Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0(T) = T and ∆n(T) = ∆(∆n−1(T)), n ∈ N. In this paper we make a brief survey on the known properties and applications of …
Rational Functions Associated To The White Noise Space And Related Topics, Daniel Alpay, David Levanony
Rational Functions Associated To The White Noise Space And Related Topics, Daniel Alpay, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
Motivated by the hyper-holomorphic case we introduce and study rational functions in the setting of Hida’s white noise space. The Fueter polynomials are replaced by a basis computed in terms of the Hermite functions, and the Cauchy-Kovalevskaya product is replaced by the Wick product.
A Characterization Of Schur Multipliers Between Character-Automorphic Hardy Spaces, Daniel Alpay, M. Mboup
A Characterization Of Schur Multipliers Between Character-Automorphic Hardy Spaces, Daniel Alpay, M. Mboup
Mathematics, Physics, and Computer Science Faculty Articles and Research
We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.
N-Linear Algebra Of Type Ii, Florentin Smarandache, W.B. Vasantha Kandasamy
N-Linear Algebra Of Type Ii, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of type II which is introduced in this book. In case of n-linear algebra of type II, we are in a position to define linear functionals which is one of the marked difference between the n-vector spaces of type I and II. However all the applications mentioned in n-linear algebras of type I can be appropriately extended to …
Special Classes Of Set Codes And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Special Classes Of Set Codes And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors introduce the notion of set codes, set bicodes and set n-codes. These are the most generalized notions of semigroup n-codes and group n-codes. Several types of set ncodes are defined. Several examples are given to enable the reader to understand the concept. These new classes of codes will find applications in cryptography, computer networking (where fragmenting of codes is to be carried out) and data storage (where confidentiality is to be maintained). We also describe the error detection and error correction of these codes. The authors feel that these codes would be appropriate to the …
Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra
Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra
Mathematics Faculty Works
The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.
Cohomology Of Categorical Self-Distributivity, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Masahico Saito
Cohomology Of Categorical Self-Distributivity, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Masahico Saito
Mathematics Faculty Works
We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provide solutions of the Yang–Baxter equation, and, conversely, solutions of the Yang–Baxter equation can be used to construct self-distributive operations in certain categories. Moreover, we present a cohomology theory that encompasses both Lie algebra and quandle cohomologies, is analogous to Hochschild cohomology, and can be used to study deformations of these self-distributive structures. All …
Value Monoids Of Zero-Dimensional Valuations Of Rank 1, Edward Mosteig
Value Monoids Of Zero-Dimensional Valuations Of Rank 1, Edward Mosteig
Mathematics Faculty Works
Classically, Grobner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build on these ideas by providing a class of valuations on k(x, y) that are suitable for this framework. For these valuations, we compute ν(k[x, y] ∗ ) and use this to perform computations concerning ideals in the polynomial ring k[x, y]. Interestingly, for these valuations, some ideals have a finite Grobner basis with respect to the valuation that is not …
Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal
Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal
Branch Mathematics and Statistics Faculty and Staff Publications
The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. He wanted them to be equipped in a branch of mathematics that was increasingly valuable for the analysis of scientific data. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. We do not indulge in labourious use of suffixes or …
Super Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy
Super Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such a paradigm shift is essential in this computerized …
N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …
Polynomial Extension Operators. Part I, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl
Polynomial Extension Operators. Part I, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl
Mathematics and Statistics Faculty Publications and Presentations
In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to introducing our new technique for constructing the extensions, and its application to the case of polynomial extensions from H½(∂K) into H¹(K), for any tetrahedron K.
A Mixed Method For Axisymmetric Div-Curl Systems, Dylan M. Copeland, Jay Gopalakrishnan, Joseph E. Pasciak
A Mixed Method For Axisymmetric Div-Curl Systems, Dylan M. Copeland, Jay Gopalakrishnan, Joseph E. Pasciak
Mathematics and Statistics Faculty Publications and Presentations
We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties.