Let S be a semigroup. A (right) S-act X is a representation of S by transformations on X. S-acts can be regarded as (unary) algebras in their own right. Thus we can talk about subacts, homomorphisms, quotients, generating sets and defining relations for S-acts. This in turn opens up a possibility of attempting to study/understand/classify semigroups according to properties of their S-acts. In this talk I will report on some recent work on some such properties: - Noetherian: S is Noetherian if every finitely generated S-act is finitely presented; - Coherent: S is coherent if every finitely generated subact of a finitely presented S-act is finitely presented; - The trivial S-act is finitely presented; - Pseudofiniteness: the trivial S-act is finitely presented and there is a uniform bound on the length of derivation sequences. I will also indicate some intriguing open problems that have arisen in each area. This work is currently being pursued under an EPSRC-funded project held jointly with Victoria Gould from York, and involves several collaborators, including Matthew Brookes, Craig Miller, James East and Thomas Quinn-Gregson.
Semigroup actions and finiteness conditions Sponsored by the Meyer Fund
Nov. 07, 2023 2:30pm (MATH 3…
Lie Theory
Chris Eblen (CU)
X
The classical case of Schur--Weyl duality links the representation theory of the general linear group to that of the symmetric group, enabling the study of both simultaneously. Generalizations of this kind of duality have yielded pathways to study the representation theory of some common groups in interesting ways. Such pathways are especially valuable when the group in question has an intractable representation theory, as in the case of the group of unipotent upper triangular matrices with entries in a finite field, . We discuss an analogue of Schur--Weyl duality for and a class of -modules called beach modules arising from the study of this duality within the framework of a particular supercharacter theory for .
Unipotent Beach Modules and Schur--Weyl Duality
Nov. 07, 2023 3:30pm (MATH 3…
Topology
Rachel Chaiser
X
I will give an introduction to the K-theory of Banach algebras, with a C*-algebraic lean. I will define Banach algebras and C*-algebras, so prior knowledge of these is helpful but not required. I will also discuss the relationship between K-theory for C*-algebras and K-theory for topological spaces.
Semigroup actions and finiteness conditions