Title

Representations of Algebras

Document Type

Oral Presentation

Campus where you would like to present

Ellensburg

Event Website

https://digitalcommons.cwu.edu/source

Start Date

16-5-2021

End Date

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.

Faculty Mentor(s)

Danny Lara

Department/Program

Mathematics

Additional Mentoring Department

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

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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