The algebraic and geometric classification of antiassociative algebras

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).

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

References in corpus (5)

• The algebraic and geometric classification of nilpotent anticommutative algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• Non-associative central extensions of null-filiform associative algebras
• The variety of dual mock-Lie algebras
• On certain classes of algebras in which centralizers are ideals

Cited by in corpus (2)

• The algebraic and geometric classification of transposed Poisson algebras
• Non-associative algebraic structures: classification and structure