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The geometric classification of 2-step nilpotent algebras and applications

Revista Matemática Complutense. 2022. Vol. 35. No. 3. P. 907–922.
Ignatyev Mikhail, Kaygorodov I., Popov Y.

We give a geometric classification of complex n-dimensional 2-step nilpotent (all, commutative and anticommutative) algebras. Namely, it has been found the number of irreducible components and their dimensions. As a corollary, we have a geometric classification of complex 5-dimensional nilpotent associative algebras. In particular, it has been proven that this variety has 11 irreducible components and 7 rigid algebras.

Research target: Mathematics
Language: English
DOI
Text on another site
Keywords: associative algebrasIrreducible componentsdegenerationNilpotent algebra2-step nilpotent algebrageometric classification
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