Some Classes of Nilpotent Associative Algebras

@article{Karimjanov2020SomeCO,
  title={Some Classes of Nilpotent Associative Algebras},
  author={I. A. Karimjanov and Manuel Ladra},
  journal={Mediterranean Journal of Mathematics},
  year={2020},
  volume={17},
  pages={1-21}
}
In this paper, we classify filiform associative algebras of degree p over a field of characteristic zero. Moreover, over an algebraically closed field of characteristic zero, we also classify filiform nilpotent associative algebras and naturally graded quasi-filiform nilpotent associative algebras, described through the characteristic sequence $$C({\mathcal {A}})=(n-2,1,1)$$ C ( A ) = ( n - 2 , 1 , 1 ) or $$C({\mathcal {A}})=(n-2,2)$$ C ( A ) = ( n - 2 , 2 ) . 
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References

SHOWING 1-10 OF 23 REFERENCES
Naturally graded quasi-filiform Lie algebras
Nilpotent associative algebras and coclass theory
Complex Structures on Quasi-filiform Lie Algebras
The aim of this article is to classify quasi-filiform nilpotent Lie algebras g , that is with nilindex dimg − 2, admitting a complex structure. Note that the non-existence of complex structures over…
Naturally graded quasi-filiform Leibniz algebras
Coclass Theory for Finite Nilpotent Associative Algebras: Algorithms and a Periodicity Conjecture
TLDR
Two algorithms are described that allow to investigate the graph associated with the nilpotent associative -algebras of coclass r for a finite field and a non-negative r to conjecture that the periodicity conjecture holds, which suggests that for each finiteField and each r the infinitely many nilpotents of cocclass r can be classified by a finite set of data.
Lie nilpotent and solvable associative algebras
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.
The algebraic and geometric classification of associative algebras of dimension five
The scheme Alg5 of associative, unitary algebra structures on k5, k an algebraically closed field with char (k)≠2 is investigated. We establish the list of GL5-orbits on Alg5 under the action of…
Classification of Lie algebras with naturally graded quasi-filiform nilradicals
Naturally Graded 2-Filiform Leibniz Algebras
In the present article the classification of naturally graded 2-filiform Leibniz algebras is obtained. A splitting of the set of naturally graded Leibniz algebras into the families of Lie and non-Lie…
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