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Articles 1 - 13 of 13
Full-Text Articles in Algebra
The Galois Correspondence For Branched Covering Spaces And Its Relationship To Hecke Algebras, Matthew Ong
The Galois Correspondence For Branched Covering Spaces And Its Relationship To Hecke Algebras, Matthew Ong
Mathematical Sciences Technical Reports (MSTR)
There is a very beautiful correspondence between branched covers of the Riemann sphere P1 and subgroups of the fundamental group π1(P1 − {branch points}), exactly analogous to the correspondence between subfields of an algebraic extension E/F and subgroups of the Galois group Gal(E/F). This paper explores the concept of a Hecke algebra, which in this context is a generalization of the Galois group to the case of non- Galois covers S/P1. Specifically, we show that the isomorphism type of a Hecke algebra C[H\G/H] is completely determined by the decomposition of …
Tilings Of Low-Genus Surfaces By Quadrilaterals, John Gregoire, Isabel Averil
Tilings Of Low-Genus Surfaces By Quadrilaterals, John Gregoire, Isabel Averil
Mathematical Sciences Technical Reports (MSTR)
In contribution to the classification of all tilings of low-genus surfaces, the kaleidoscopic and non-kaleidoscopic tilings by quadrilaterals are given up to genus 12. As part of their classification, the algebraic structure of the conformal tiling groups and the geometric structure of the tiles are specified. In addition, several infinite classes of tilings and tiling groups are presented.
Central Twisted Transformation Groups And Group C*-Algebras Of Central Group Extensions, Siegfried Echterhoff, Dana P. Williams
Central Twisted Transformation Groups And Group C*-Algebras Of Central Group Extensions, Siegfried Echterhoff, Dana P. Williams
Dartmouth Scholarship
We examine the structure of central twisted transformation group C∗-algebras C0(X) ⋊id,u G, and apply our results to the group C ∗-algebras of central group extensions. Our methods require that we study Moore’s cohomology group H2 (G, C(X,T)), and, in particular, we prove an inflation result for pointwise trivial cocyles which may be of use elsewhere.
On Graphs With Equal Algebraic And Vertex Connectivity, Stephen J. Kirkland, Jason J. Molitierno, Michael Neumann, Bryan L. Shader
On Graphs With Equal Algebraic And Vertex Connectivity, Stephen J. Kirkland, Jason J. Molitierno, Michael Neumann, Bryan L. Shader
Mathematics Faculty Publications
No abstract provided.
Definability, Canonical Models, And Compactness For Finitary Coalgebraic Modal Logic, Alexander Kurz, Dirk Pattinson
Definability, Canonical Models, And Compactness For Finitary Coalgebraic Modal Logic, Alexander Kurz, Dirk Pattinson
Engineering Faculty Articles and Research
This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours is defined. We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Behω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence.
Modal Predicates And Coequations, Alexander Kurz, Jiří Rosický
Modal Predicates And Coequations, Alexander Kurz, Jiří Rosický
Engineering Faculty Articles and Research
We show how coalgebras can be presented by operations and equations. This is a special case of Linton’s approach to algebras over a general base category X, namely where X is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic.
A Density Property Of The Tori And Duality, Peter Loth
A Density Property Of The Tori And Duality, Peter Loth
Mathematics Faculty Publications
In this note, a short proof of a recent theorem of D. Dikranjan and M. Tkachenko is given, and their result is extended.
Some Extensions Of Loewner's Theory Of Monotone Operator Functions, Daniel Alpay, Vladimir Bolotnikov, A. Dijksma, J. Rovnyak, A. Dijksma
Some Extensions Of Loewner's Theory Of Monotone Operator Functions, Daniel Alpay, Vladimir Bolotnikov, A. Dijksma, J. Rovnyak, A. Dijksma
Mathematics, Physics, and Computer Science Faculty Articles and Research
Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalar- to matrix-valued functions of an operator argument. A notion of -monotonicity is introduced and characterized in terms of classical Nevanlinna functions with removable singularities on a real interval. Corresponding results for Stieltjes functions are presented.
Fundamental Theorem Of Algebra, Paul Shibalovich
Fundamental Theorem Of Algebra, Paul Shibalovich
Theses Digitization Project
The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.
Preface, Alexander Kurz
Preface, Alexander Kurz
Engineering Faculty Articles and Research
No abstract provided.
Some Irrational Generalised Moonshine From Orbifolds, Rossen Ivanov, Michael Tuite
Some Irrational Generalised Moonshine From Orbifolds, Rossen Ivanov, Michael Tuite
Articles
We verify the Generalised Moonshine conjectures for some irrational modular functions for theMonster centralisers related to the Harada-Norton, Held, M12 and L3(3) simple groups based on certain orbifolding constraints. We find explicitly the fixing groups of the hauptmoduls arising in each case.
Rational Generalized Moonshine From Abelian Orbifoldings Of The Moonshine Module, Rossen Ivanov, Michael Tuite
Rational Generalized Moonshine From Abelian Orbifoldings Of The Moonshine Module, Rossen Ivanov, Michael Tuite
Articles
We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational …
A Note On Interpolation In The Generalized Schur Class. I. Applications Of Realization Theory, Daniel Alpay, T. Constantinescu, A. Dijksma, J. Rovnyak, A. Dijksma
A Note On Interpolation In The Generalized Schur Class. I. Applications Of Realization Theory, Daniel Alpay, T. Constantinescu, A. Dijksma, J. Rovnyak, A. Dijksma
Mathematics, Physics, and Computer Science Faculty Articles and Research
Realization theory for operator colligations on Pontryagin spaces is used to study interpolation and factorization in generalized Schur classes. Several criteria are derived which imply that a given function is almost the restriction of a generalized Schur function. The role of realization theory in coefficient problems is also discussed; a solution of an indefinite Carathéodory-Fejér problem is obtained, as well as a result that relates the number of negative (positive) squares of the reproducing kernels associated with the canonical coisometric, isometric, and unitary realizations of a generalized Schur function to the number of negative (positive) eigenvalues of matrices derived from …