The geometric classification of nilpotent commutative $\mathfrak{CD}$-algebras

Doston Jumaniyozov; Ivan Kaygorodov; Abror Khudoyberdiyev

doi:10.1007/s40574-021-00313-5

The geometric classification of nilpotent commutative $\mathfrak{CD}$-algebras

Rings and Algebras 2022-04-04 v1

Authors: Doston Jumaniyozov , Ivan Kaygorodov , Abror Khudoyberdiyev

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Abstract

We give a geometric classification of complex $5$ -dimensional nilpotent commutative $\mathfrak{CD}$ -algebras. The corresponding geometric variety has dimension $24$ and decomposes into $10$ irreducible components determined by the Zariski closures of a two-parameter family of algebras, three one-parameter families of algebras, and $6$ rigid algebras.

Keywords

nilpotent commutative algebras cd-algebras geometric classification zariski closure irreducible components 5-dimensional algebras

Cite

@article{arxiv.2110.12849,
  title  = {The geometric classification of nilpotent commutative $\mathfrak{CD}$-algebras},
  author = {Doston Jumaniyozov and Ivan Kaygorodov and Abror Khudoyberdiyev},
  journal= {arXiv preprint arXiv:2110.12849},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2007.01829, arXiv:2103.01036, arXiv:2001.00253, arXiv:2006.00734; text overlap with arXiv:2109.00483

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