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 structure constants which is helpful in solving many other problems related to two-dimensional algebras.
REFERENCES
1.
Ahmed
, H.
, Bekbaev
, U.
, Rakhimov
, I.
: Complete classification of two-dimensional algebras, 12 pages
, AIP Conference Proceedings
, 1830
, 070016
, 2017
, doi .2.
Ahmed
, H.
, Bekbaev
, U.
, Rakhimov
, I.
: Classification of 2-dimensional evolution algebras, their groups of automorphisms and derivation algebras
, Journal of Physics Conference Series
, 1489
(2020
) 012001
, doi:.3.
Ahmed
, H.
, Bekbaev
, U.
, Rakhimov
, I.
: Identities on Two-Dimensional Algebras
, Lobachevskii Journal of Mathematics
, 2020
, 41
(9
), 1615
–1629
.4.
Ahmed
, H.
, Bekbaev
, U.
, Rakhimov
, I.
: Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras
, International Journal of Algebra and Computations
, 2020
, 30
(5
), 903
–929
.5.
Ahmed
, H.
, Bekbaev
, U.
, Rakhimov
, I.
: On Two-Dimensional Power Associative Algebras Over Algebraically Closed Fields and R
, Lobachevskii Journal of Mathematics
, 2019
, 40
(1
), 1
–13
.6.
Ahmed
, H.
, Bekbaev
, U.
, Rakhimov
, I.
: Classification of two-dimensional Jordan algebras over R
, Malaysian Journal of Mathematical Sciences
, 2018
, 12
(3
), 287
–303
.7.
Althoen
, S.C.
, Hansen
, K.D.
: Two-dimensional real algebras with zero divisors
. Acta Sci. Math
(Szeged) 56
, 23
–42
(1992
)8.
Bekbaev
, U.
: On classification of m-dimensional algebras
, Journal of Physics: Conf. Series
, 819
(2017
) 012012
doi:.9.
Bekbaev
, U.
: Complete classifications of two-dimensional general, commutative, commutative Jordan, division and evolution real algebras.
ArXiv: 1705 01237[math.RA]10.
Kaygorodov
, I.
, Volkov
, Yu
. : The variety of 2-dimensional algebras over an algebraically closed field
, Canadian Journal of Mathematics
, 2019
, 71
(4
), 819
–842
.11.
Petersson
, H.P.
: The classification of two-dimensional nonassicative algebras
, 2000
, Result. Math.
, 3
, 120
–154
.12.
Petersson
, H.P.
, Scherer
, M.
: The number of nonisomorphic two-dimensional algebras over a finite field
. Results Math.
42
(1–2
), 137
–152
(2004
)13.
Verhulst
, N.D.
: Counting Finite-Dimensional Algebras Over Finite Fields
, Results Math.
(2020
) 75
:153
This content is only available via PDF.
©2023 Authors. Published by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.