Al-Essa Dissertation on Modules over Infinite Dimensional Algebras, March 13

A Mathematics Dissertation Defense by Lulwah Al-Essa is Friday March 13, at 2 p.m. in Morton 322.

Al-Essa’s presentation on “Modules over Infinite Dimensional Algebras” is directed by Dr. Sergio Lopez-Permouth.

Abstract: Let A be an infinite dimensional K- algebra, where K is a field and let B be a basis for A. In this dissertation, 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 present several examples in the familiar setting of the algebra K[x] of polynomials with coefficients in K and the Laurent Polynomial Algebra K[x, x^{−1}]. Finally, we introduce some results regarding these notions in the context of Leavitt Path Algebras.