Representations of Algebras

Author(s)

Adara Andonie

Faculty Mentor(s)

Danny Lara (Mathematics)

Abstract

Arbitrary finite dimensional K-algebras have been classified into three types by the famous theorem of Drozd by their representation type. These categories are Representation Finite, Tame, and Wild. Our focus is on Algebras of Wild Representation type. As the name suggest, the indecomposable representations of these algebras are not feasible to classify. In fact, it’s impossible. However, Dense Orbit Algebras that are of wild representation type seem to have finitely many representations (up to a certain equivalence) that satisfy a geometric property. There are very few examples of such algebras in the current literature. We explore a particular algebra of wild representation type and show, via a computational algorithm, that the algebra is a Dense Orbit Algebra.

Keywords: Dense, Algebras, Computer algorithm

Presentation

3 thoughts on “Representations of Algebras”

  1. This is a complex and ambitious research, involving both abstract algebra and computer programming. The major difficulty comes from the advanced mathematical concepts handled, most of them above the level of an undergraduate student.
    Congratulations on your excellent work and results! A special remark on the patience and enthusiasm of your advisor, Dr. Danny Lara, who proves to be a great mentor. Interesting, this is the only SOURCE 2021 pure mathematics presentation.

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