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Computing with Matrix and Basic Algebras

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Advances in Algebra (SRAC 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 277))

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Abstract

This is a survey of my lecture delivered at the Southern Regional Algebra Conference in March 2017. It is meant to demonstrate some of the methods and technology that can be used to investigate examples in the theory of representations of groups and algebras. The concentration is on using computational methods to determine the structure of a matrix algebra as in the theorems of Wedderburn and investigating homological properties of the algebra by way of its basic algebra. For every split finite-dimensional associative algebra, there is a basic algebra, one whose simple modules have dimension one, that has the same representation theory. In the computational setting, it is usually much more practical to first find the basic algebra when studying representation theory.

Research partially funded by Simonds Foundation Grant No. 054813-01

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA

    Jon F. Carlson

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  1. Jon F. Carlson
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Correspondence to Jon F. Carlson .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA

    Jörg Feldvoss

  2. Department of Mathematics, Spring Hill College, Mobile, AL, USA

    Lauren Grimley

  3. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA

    Drew Lewis

  4. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA

    Andrei Pavelescu

  5. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA

    Cornelius Pillen

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Carlson, J.F. (2019). Computing with Matrix and Basic Algebras. In: Feldvoss, J., Grimley, L., Lewis, D., Pavelescu, A., Pillen, C. (eds) Advances in Algebra. SRAC 2017. Springer Proceedings in Mathematics & Statistics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-030-11521-0_5

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