The algebraic classification of nilpotent commutative algebras

Doston Jumaniyozov; Ivan Kaygorodov; Abror Khudoyberdiyev; Doston Jumaniyozov; Ivan Kaygorodov; Abror Khudoyberdiyev

doi:10.3934/era.2021068

Electronic Research Archive

2021, Volume 29, Issue 6: 3909-3993. doi: 10.3934/era.2021068

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The algebraic classification of nilpotent commutative algebras

1.
National University of Uzbekistan, Tashkent, Uzbekistan, Institute of Mathematics named after V.I. Romanovsky Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan
2.
CMCC, Universidade Federal do ABC, Santo André, Brazil, Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia, Saint Petersburg University, Russia
3.
National University of Uzbekistan, Tashkent, Uzbekistan, Institute of Mathematics named after V.I. Romanovsky, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

Received: 01 February 2021 Revised: 01 July 2021 Published: 07 September 2021
Primary: 17A01; Secondary: 17D99, 17A99

This paper is devoted to the complete algebraic classification of complex $ 5 $-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller nilpotent commutative algebras and the recently obtained classification of complex $ 5 $-dimensional nilpotent commutative $ \mathfrak{CD} $-algebras.
- Commutative algebras,
- Jordan algebras,
- nilpotent algebras,
- algebraic classification,
- central extension
Citation: Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev. The algebraic classification of nilpotent commutative algebras[J]. Electronic Research Archive, 2021, 29(6): 3909-3993. doi: 10.3934/era.2021068

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Abstract

This paper is devoted to the complete algebraic classification of complex $ 5 $-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller nilpotent commutative algebras and the recently obtained classification of complex $ 5 $-dimensional nilpotent commutative $ \mathfrak{CD} $-algebras.

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