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.

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.
You do not currently have access to this content.