The Algebra Seminar series presents Ben Stanley, discussing “Amenability and Congeniality: A Topological Perspective” on Tuesday, April 18, from 4:30-5:30 p.m. in Morton 313.
Stanley is a graduate student in Mathematics at Ohio University.
Abstract: Let A be a countably infinite dimensional K-algebra, where K is a field and let B be a basis for A. We explore the situation when B is such that K^B (the direct product indexed by B of copies of the field K) can be made into an A-module in a natural way. We call such a basis B amenable. In exploring the question of when two such bases, B and C, yield so-called basic modules which are isomorphic, the notion of congenial bases was introduced. These properties seem to be primarily related to the product topologies on K^B and K^C where each copy of K is given the discrete topology. Let K^(B) and K^(C) be the subspaces of K^B, K^C that consists of sequences with finite support. When the bases B and C are countable, amenability and congeniality may be fully characterized in topological terms via uniform continuity. Thus, it is natural to study a topological category with basic modules as objects and uniformly continuous morphisms.