Conservative algebras of $2$-dimensional algebras, IV
Rings and Algebras
2023-12-04 v1
Abstract
The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he 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). It looks like in the theory of conservative algebras plays a similar role to the role of in the theory of Lie algebras. Namely, an arbitrary conservative algebra can be obtained from a universal algebra for some The present paper is a part of a series of papers, dedicated to the study of the algebra and its principal subalgebras.
Cite
@article{arxiv.2212.00415,
title = {Conservative algebras of $2$-dimensional algebras, IV},
author = {Amir Fernández Ouaridi and Ivan Kaygorodov and Cándido Martín González},
journal= {arXiv preprint arXiv:2212.00415},
year = {2023}
}