On classification of finite dimensional algebras

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.

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

References in corpus (1)

• Generic algebras: rational parametrization and normal forms

Cited by in corpus (2)

• Complete classifications of two-dimensional general, commutative, commutative Jordan, division and evolution real algebras
• Two-dimensional left (right) unital algebras over algebraically closed fields and $\mathbb{R}$