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arXiv · 2401.10243

The algebraic and geometric classification of antiassociative algebras

Renato Fehlberg Júnior·Ivan Kaygorodov·Crislaine Kuster
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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).

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Renato Fehlberg Júnior, Ivan Kaygorodov, Crislaine Kuster. 2023-12-01. The algebraic and geometric classification of antiassociative algebras. https://doi.org/10.1007/s13398-022-01218-4

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