Modules over infinite dimensional algebras, by Lulwah Al-Essa (Ohio University)
Apr 10, 2014
from 04:10 PM to 05:00 PM
|Contact Name||Sergio R. Lopez|
|Contact Phone||740 593 1258|
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Abstract: Let A be an infinite dimensional K- algebra, where K is a field and let B be a basis for A. In this talk we explore a property of the basis B that guarantees that K^B (the direct product of copies indexed by B of the field K) can be made into an A-module in a natural way. We call bases satisfying that property “amenable” and we show that not all amenable bases yield isomorphic A-modules. Then we consider a relation (which we name congeniality) that guarantees that two different bases yield isomorphic A-module structures on K^B. We will look at several examples in the familiar setting of the algebra K[x] of polynomials with coefficients in K. If time allows it, we will discuss some results regarding these notions in the context of Leavitt Path Algebras.
(joint work with Sergio R. L\’opez-Permouth and Najat Muthana)