### Electronic Research Archive

2021, Issue 6: 3909-3993. doi: 10.3934/era.2021068
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# The algebraic classification of nilpotent commutative algebras

• 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.

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

### Related Papers:

• 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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