Algebra Commons^™

Linear Algebra By Analogy, Scott H. Hochwald

Scott H. Hochwald

No abstract provided.

More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

We find an upper bound on the probability that a randomly selected triple in a group is 3-rewriteable, and a bound for the core set rewriteability.

Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

Our goal is to define the cyclicizer, which is analogous to the centralizer and normalizer, and to examine groups in which these subsets have certain special properties.

Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman

Mathematical Sciences Technical Reports (MSTR)

We discuss various results on the number of commuting pairs and the sizes of the centralizers of a group.

An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg

Mathematical Sciences Technical Reports (MSTR)

An ordered triple of group elements (x,y,z) is said to be rewriteable if the product xyz is equal to one of the products xzy, yxz, yzx, zxy, zyx. In the present paper, we shall ask the following question: how rewriteable can a finite group be if its derived group has order greater than 2?

Finite Abelian Groups In Which The Probability Of An Automorphism Fixing An Element Is Large, Gary J. Sherman

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group and let A be its automorphism group. We obtain various results on the probability that a random element of A fixes a random element of G.

Moore Cohomology, Principal Bundles, And Actions Of Groups On C*-Algebras, Ian Raeburn, Dana P. Williams

Dartmouth Scholarship

In recent years both topological and algebraic invariants have been associated to group actions on C*-algebras. Principal bundles have been used to describe the topological structure of the spectrum of crossed products [18, 19], and as a result we now know that crossed products of even the very nicest non-commutative algebras can be substantially more complicated than those of commutative algebras [19, 5]. The algebraic approach involves group cohomological invariants, and exploits the associated machinery to classify group actions on C*-algebras; this originated in [2], and has been particularly successful for actions of R and tori ([19; Section 4], [21]). …

Modern Algebra And Discrete Structures, R. F. Lax

E-Textbooks

This text is intended for either an applied algebra course or a modern algebra course that includes more applications than has been traditional. It is at an advanced undergraduate (junior-senior) level and is suitable for a one-semester or two-quarter course. We assume that students have already had a course in linear algebra (although we briefly review concepts from linear algebra when they are needed in the sections on fields and linear codes).

Our treatment is fairly rigorous, with almost every proof supplied. However, we have tried to concentrate on examples and applications. In an applied algebra course, which usually consists …

Analytic Continuation In Bergman Spaces And The Compression Of Certain Toeplitz Operators, William T. Ross

Department of Math & Statistics Faculty Publications

Let G be a Jordan domain and K C G be relatively closed with Area(K) = 0. Let A² (G\K) and A²(G) be the Bergman spaces on G\K, respectively G and define N = A²(G\K) Ɵ A² (G). In this paper we show that with a mild restriction on K, every function in N has an analytic continuation across the analytic arcs of aG that do not intersect K. This result will be used to discuss the Fredholm theory of the operator C_f = P_NT_f│N, where f ϵ C(G) …

Some Remarks On Reproducing Kernel Krein Spaces, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

The one-to-one correspondence between positive functions and reproducing kernel Hilbert spaces was extended by L. Schwartz to a (onto, but not one-to-one) correspondence between difference of positive functions and reproducing kernel Krein spaces. After discussing this result, we prove that matrix value function K(z,ω) symmetric and jointly analytic in z and ω in a neighborhood of the origin is the reproducing kernel of a reproducing kernel Krein space. We conclude with an example showing that such a function can be the reproducing kernel of two different Krein spaces.