Conservative algebras of $2$-dimensional algebras, II
Rings and Algebras
2020-04-03 v1
Abstract
In 1990 Kantor defined the conservative algebra of all algebras (i.e. bilinear maps) on the -dimensional vector space. If , then the algebra does not belong to any well-known class of algebras (such as associative, Lie, Jordan, or Leibniz algebras). We describe automorphisms, one-sided ideals, and idempotents of Also similar problems are solved for the algebra of all commutative algebras on the 2-dimensional vector space and for the algebra of all commutative algebras with trace zero multiplication on the 2-dimensional vector space.
Keywords
Cite
@article{arxiv.1507.02324,
title = {Conservative algebras of $2$-dimensional algebras, II},
author = {Ivan Kaygorodov and Yury Volkov},
journal= {arXiv preprint arXiv:1507.02324},
year = {2020}
}