Classification in a rotational flow of two-dimensional algebras

TL;DR

This paper studies a family of two-dimensional algebras evolving over time, showing most are non-isomorphic and including a commutative case, while comparing with existing classifications.

Contribution

It introduces a time-dependent flow of 2D algebras and characterizes their isomorphism classes, revealing uncountably many non-isomorphic algebras.

Findings

Flow contains uncountably many non-isomorphic algebras

Includes at least one commutative algebra

Provides comparison with existing classifications

Abstract

In this paper, we examine a time-dependent family of two-dimensional algebras. We investigate the conditions under which any two algebras from this family, formed at different times, are isomorphic. Our findings reveal that the flow comprises of uncountable pairwise non-isomorphic algebras, including one commutative algebra. Additionally, we compare our results with a previously established classification of 2-dimensional real algebras.