## May 2021 College of the Sciences Presentations

#### Title

Representations of Algebras

#### Document Type

Oral Presentation

Ellensburg

#### Event Website

https://digitalcommons.cwu.edu/source

16-5-2021

22-5-2021

#### Keywords

Dense, Algebras, Computer algorithm

#### 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.

Danny Lara

Mathematics

#### Additional Mentoring Department

https://cwu.studentopportunitycenter.com/representations-of-algebras/

#### Share

COinS

May 16th, 12:00 PM May 22nd, 12:00 PM

Representations of Algebras

Ellensburg

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.

https://digitalcommons.cwu.edu/source/2021/COTS/69