On classification of m-dimensional algebras

A constructive approach to the classification and invariance problems, with respect to basis changes, of the finite dimensional algebras is offered. A construction of an invariant open, dense (in the Zariski topology) subset of the space of structure constants of algebras is given. A classification...

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Bibliographic Details
Published in:Journal of physics. Conference series 2017-03, Vol.819 (1), p.12012
Main Author: Bekbaev, U.
Format: Article
Language:English
Subjects:
Algebra
Classification
Dimensional changes
Invariants
Physics
Rational functions
Topology
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Summary:A constructive approach to the classification and invariance problems, with respect to basis changes, of the finite dimensional algebras is offered. A construction of an invariant open, dense (in the Zariski topology) subset of the space of structure constants of algebras is given. A classification of all algebras with structure constants from this dense set is given by providing canonical representatives of their orbits. A finite system of generators for the corresponding field of invariant rational functions of structure constants is shown.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/819/1/012012