On classification of finite dimensional algebras
Rings and Algebras
2015-09-24 v3
Abstract
Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with structural constants from this set are classified and a basis to the field of invariant rational functions of structural constants is provided.
Keywords
Cite
@article{arxiv.1504.01194,
title = {On classification of finite dimensional algebras},
author = {Ural Bekbaev},
journal= {arXiv preprint arXiv:1504.01194},
year = {2015}
}
Comments
The main changes are due to the drop of the statement on rationality of the extension $F\subset F(x)^{GL(m,F)}$ from Theorem 2.2 because lack of justification. In section 2 instead of $GL(m,F)$ any algebraic subgroup $G$ of it is considered