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arXiv · 2007.01829

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

Ivan Kaygorodov·Mykola Khrypchenko
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Abstract

We give a geometric classification of complex $4$-dimensional nilpotent $\mathfrak{CD}$-algebras. The corresponding geometric variety has dimension 18 and decomposes into $2$ irreducible components determined by the Zariski closures of a two-parameter family of algebras and a four-parameter family of algebras (see Theorem 2). In particular, there are no rigid $4$-dimensional complex nilpotent $\mathfrak{CD}$-algebras.

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Ivan Kaygorodov, Mykola Khrypchenko. 2020-07-01. The geometric classification of nilpotent $\mathfrak{CD}$-algebras. https://doi.org/10.1142/s021949882150198x

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