[PDF][PDF] Complete classification of two-dimensional algebras over any basic field

U Bekbaev - AIP Conference Proceedings, 2023 - researchgate.net
This paper is about the classification, up to isomorphism, of two-dimensional algebras over
any basic field. It provides a full classification of such algebras in terms of their matrices of …

Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras

H Ahmed, U Bekbaev, I Rakhimov - International Journal of Algebra …, 2020 - World Scientific
All subalgebras, idempotents, left (right) ideals and left quasi-units of two-dimensional
algebras are described. Classifications of algebras with given number of subalgebras, left …

Varieties of bicommutative algebras

V Drensky - arXiv preprint arXiv:1706.04279, 2017 - arxiv.org
Bicommutative algebras are nonassociative algebras satisfying the polynomial identities of
right-and left-commutativity (xy) z=(xz) y and x (yz)= y (xz). We study subvarieties of the …

A complete classification of two-dimensional endo-commutative algebras over an arbitrary field

D Asrorov, U Bekbaev, I Rakhimov - arXiv preprint arXiv:2304.00491, 2023 - arxiv.org
In the paper, we consider the class of so-called endo-commutative algebras. From the
identity imposed to specify this class, one can easily see that the product in this class …

Identities on two-dimensional algebras

H Ahmed, U Bekbaev, I Rakhimov - Lobachevskii Journal of Mathematics, 2020 - Springer
Identities on Two-Dimensional Algebras | Lobachevskii Journal of Mathematics Skip to main
content SpringerLink Account Menu Find a journal Publish with us Track your research Search …

3-dimensional skew-symmetric algebras and the variety of Hom-Lie algebras

E Remm - Algebra Colloquium, 2018 - World Scientific
An algebra is called skew-symmetric if its multiplication operation is a skewsymmetric
bilinear application. We determine all these algebras in dimension 3 over a field of …

On two-dimensional power associative algebras over algebraically closed fields and R

H Ahmed, U Bekbaev, I Rakhimov - Lobachevskii Journal of Mathematics, 2019 - Springer
In this paper we describe all power-associative algebra structures on a two-dimensional
vector space over algebraically closed fields and ℝ. The list of all two-dimensional left (right) …

[PDF][PDF] The automorphism groups and derivation algebras of two-dimensional algebras

H Ahmed, U Bekbaev, I Rakhimov - arXiv preprint arXiv:1708.01376, 2017 - arxiv.org
arXiv:1708.01376v2 [math.RA] 7 Dec 2018 Page 1 arXiv:1708.01376v2 [math.RA] 7 Dec 2018
In the name of Allah, the Beneficent, the Merciful. THE AUTOMORPHISM GROUPS AND …

On classification of m-dimensional algebras

U Bekbaev - Journal of Physics: Conference Series, 2017 - iopscience.iop.org
A constructive approach to the classification and invariance problems, with respect to basis
changes, of the finite dimensional algebras is offered. A construction of an invariant open …

[PDF][PDF] Classification of two-dimensional Jordan algebras over R

H Ahmed, U Bekbaev, I Rakhimov - Malaysian Journal of …, 2018 - mjms.upm.edu.my
Classification of Two-Dimensional Jordan Algebras Over R Page 1 Malaysian Journal of
Mathematical Sciences 12(3): 287–303 (2018) MALAYSIAN JOURNAL OF …