The algebraic and geometric classification of nilpotent Novikov algebras

@article{Karimjanov2019TheAA,
  title={The algebraic and geometric classification of nilpotent Novikov algebras},
  author={Iqboljon Karimjanov and Ivan Kaygorodov and A. Kh. Khudoyberdiyev},
  journal={Journal of Geometry and Physics},
  year={2019}
}
Abstract This paper is devoted to the complete algebraic and geometric classification of 4-dimensional nilpotent Novikov algebras over ℂ . 
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 Bicommutative Algebras
We classify the complex 4-dimensional nilpotent bicommutative algebras from both algebraic and geometric approaches.
The geometric classification of nilpotent ℭ𝔇-algebras
We give a geometric classification of complex 4-dimensional nilpotent ℭ𝔇-algebras. The corresponding geometric variety has dimension 18 and decomposes into 2 irreducible components determined by
The geometric classification of nilpotent Tortkara algebras
Abstract We give a geometric classification of all 6-dimensional nilpotent Tortkara algebras over
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
The algebraic classification of nilpotent Tortkara algebras
Abstract We classify all complex 6-dimensional nilpotent Tortkara algebras. Communicated by Alberto Facchini
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.
One-generated nilpotent Novikov algebras
We give a classification of 5- and 6-dimensional complex one-generated nilpotent Novikov algebras
The geometric classification of nilpotent commutative CD-algebras
We give a geometric classification of complex 5-dimensional nilpotent commutative CDalgebras. The corresponding geometric variety has dimension 24 and decomposes into 10 irreducible components
One-generated nilpotent terminal algebras
Abstract We give an algebraic classification of complex 5-dimensional one-generated nilpotent terminal algebras.
...
1
2
3
4
...

References

SHOWING 1-10 OF 59 REFERENCES
Classification of Simple Novikov Algebras and Their Irreducible Modules of Characteristic 0
Abstract In this paper, we first present a classification theorem of simple infinite-dimensional Novikov algebras over an algebraically closed field of characteristic 0. Then we classify all the
Engel Theorem for Novikov Algebras
ABSTRACT We prove that, if A is left-nil Novikov algebra, then A 2 is nilpotent.
The algebraic and geometric classification of nilpotent binary Lie algebras
We give a complete algebraic classification of nilpotent binary Lie algebras of dimension at most 6 over an arbitrary field of characteristic not 2 and a complete geometric classification of
Classification of nilpotent associative algebras of small dimension
  • W. D. Graaf
  • Computer Science, Mathematics
    Int. J. Algebra Comput.
  • 2018
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.
On classification of four-dimensional nilpotent Leibniz algebras
ABSTRACT Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for
Degenerations of binary Lie and nilpotent Malcev algebras
ABSTRACT We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over ℂ. In particular, we describe all irreducible components of
On simple Novikov algebras and their irreducible modules
Abstract We give a complete classification of finite-dimensional simple Novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic. Moreover, we
Nilpotent evolution algebras over arbitrary fields
Abstract The paper is devoted to the study of annihilator extensions of evolution algebras and suggests an approach to classify finite-dimensional nilpotent evolution algebras. Subsequently nilpotent
NOVIKOV-JORDAN ALGEBRAS
ABSTRACT Algebras with the identity are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has a unit, then it is
Degenerations of Zinbiel and nilpotent Leibniz algebras
ABSTRACT We describe degenerations of four-dimensional Zinbiel and four-dimensional nilpotent Leibniz algebras over In particular, we describe all irreducible components in the corresponding
...
1
2
3
4
5
...