On classification of m-dimensional algebras

37th International Conference on Quantum Probability and Related Topics

Bekbaev, U.^1

Department of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, P.O. Box 10, Kuala Lumpur

50728, Malaysia^1

关键词: Basis changes;    Canonical representatives;    Constructive approach;    Finite systems;    Finite-dimensional algebras;    Structure constants;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/819/1/012012/pdf
DOI  :  10.1088/1742-6596/819/1/012012

来源: IOP

【 摘 要 】

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.