One-generated nilpotent terminal algebras

@article{Kaygorodov2020OnegeneratedNT,
  title={One-generated nilpotent terminal algebras},
  author={Ivan Kaygorodov and Abror Kh. Khudoyberdiyev and Aloberdi Sattarov},
  journal={Communications in Algebra},
  year={2020},
  volume={48},
  pages={4355 - 4390}
}
Abstract We give an algebraic classification of complex 5-dimensional one-generated nilpotent terminal algebras. 

One-Generated Nilpotent Bicommutative Algebras

We give a classification of 5- and 6-dimensional complex one-generated nilpotent bicommutative algebras.

One-generated nilpotent assosymmetric algebras

We give the classification of $5$- and $6$-dimensional complex one-generated nilpotent assosymmetric algebras.

The algebraic classification of nilpotent commutative -algebras

Abstract An algebraic classification of complex 5-dimensional nilpotent commutative -algebras is given. This classification is based on an algebraic classification of complex 5-dimensional nilpotent

Conservative algebras of 2-dimensional algebras, III

Abstract In the present paper we prove that every local and 2-local derivation on conservative algebras of 2-dimensional algebras are derivations. Also, we prove that every local and 2-local

Central extensions of 3-dimensional Zinbiel algebras

We describe all central extensions of all 3-dimensional non-zero complex Zinbiel algebras. As a corollary, we have a full classification of 4-dimensional non-trivial complex Zinbiel algebras and a

Central extensions of filiform Zinbiel algebras

ABSTRACT In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform Zinbiel algebras. It is proven that every non-split central extension of an

R A ] 1 S ep 2 02 0 Central extensions of filiform Zinbiel algebras

In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform Zinbiel algebras. It is proven that every non-split central extension of an n-dimensional

Conservative algebras and superalgebras: a survey

Abstract We give a survey of results obtained on the class of conservative algebras and superalgebras, as well as on their important subvarieties, such as terminal algebras.

References

SHOWING 1-10 OF 41 REFERENCES

The algebraic classification of nilpotent terminal algebras

We classify all 4-dimensional complex nilpotent terminal algebras.

One-generated nilpotent Novikov algebras

We give a classification of five- and six-dimensional complex one-generated nilpotent Novikov algebras.

The algebraic classification of nilpotent Tortkara algebras

Abstract We classify all complex 6-dimensional nilpotent Tortkara algebras. Communicated by Alberto Facchini

The Algebraic and Geometric Classification of Nilpotent Bicommutative Algebras

We classify the complex 4-dimensional nilpotent bicommutative algebras from both algebraic and geometric approaches.

The algebraic classification of nilpotent associative commutative algebras

In this paper, we give a complete algebraic classification of 5-dimensional complex nilpotent associative commutative algebras.

The Algebraic and Geometric Classification of Nilpotent Assosymmetric Algebras

We present algebraic and geometric classifications of the 4-dimensional complex nilpotent assosymmetric algebras.

The algebraic and geometric classification of nilpotent Novikov algebras

On Some Zero-Filiform Algebras

We present the description of algebras with the maximum nilpotency index given by certain special identities.

Classification of nilpotent associative algebras of small dimension

TLDR
It is shown that nilpotent associative algebras of dimensions up to 4 over any field can be classified as central extensions of algeBRas of smaller dimension, analogous to methods known fornilpotent Lie algebraes.

Non-associative central extensions of null-filiform associative algebras