Complete classification of algebras of level two
Rings and Algebras
2020-04-03 v2 Algebraic Geometry
Abstract
The main result of the paper is the classification of all (nonassociative) algebras of level two, i.e. such algebras that maximal chains of nontrivial degenerations starting at them have length two. During this classification we obtain an estimation of the level of an algebra via its generation type, i.e. the maximal dimension of its one generated subalgebra. Also we describe all degenerations and levels of algebras of the generation type with a square zero ideal of codimension .
Cite
@article{arxiv.1710.08943,
title = {Complete classification of algebras of level two},
author = {Ivan Kaygorodov and Yury Volkov},
journal= {arXiv preprint arXiv:1710.08943},
year = {2020}
}