The algebraic and geometric classification of antiassociative algebras
Rings and Algebras
2024-01-22 v1
Abstract
This paper is devoted to the complete algebraic and geometric classification of complex 4 and 5-dimensional antiassociative algebras. In particular, we proved that the variety of complex 4-dimensional antiassociative algebras has dimension 12 and it is defined by three irreducible components (in particular, there is only 1 rigid algebra in this variety); the variety of complex 5-dimensional antiassociative algebras has dimension 24 and it is defined by 8 irreducible components (in particular, there are only 4 rigid algebras in this variety).
Keywords
Cite
@article{arxiv.2401.10243,
title = {The algebraic and geometric classification of antiassociative algebras},
author = {Renato Fehlberg Júnior and Ivan Kaygorodov and Crislaine Kuster},
journal= {arXiv preprint arXiv:2401.10243},
year = {2024}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2205.00444, arXiv:2206.00315, arXiv:2307.00289, arXiv:2308.00374, arXiv:2106.00336, arXiv:1912.02691, arXiv:1812.01442