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Representations of Algebras: Some Computational Aspects

Rhoads, Kyle James
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Thesis/Dissertation
Date
2019
Advisor
Letzter, E. S. (Edward S.), 1958-
Committee member
Dolgushev, Vasily
Lorenz, Martin, 1951-
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Department
Mathematics
Subject
Mathematics
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http://hdl.handle.net/20.500.12613/2237
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Rhoads_temple_0225M_13839.pdf
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http://dx.doi.org/10.34944/dspace/2219
Abstract
Let n ϵ Z≥1 and R be a finitely presented k-algebra over a computable field k. We describe algorithms for computably deciding representation-theoretic properties of R, following work by Letzter. Among these algorithms is an algorithm deciding whether an n-dimensional irreducible representation exists. We also provide a package, finitely-presented-algebra, which implements these algorithms into the computer algebra system SAGE.
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