O‘zbekiston matematika jurnali Volume 69 Issue 4 (2025) · pp. 22-34

Classification of Frobenius algebra structures on two-dimensional vector space over any base field

Asrorov, D.U., Bekbaev, U.D., Rakhimov, I.S.

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Abstract

In this paper, we first classify all associative algebra structures on a two-dimensional vector space over an arbitrary base field equipped with a non-degenerate bilinear form. We then determine which of these are Frobenius algebras. We provide lists of canonical representatives of the isomorphism classes of these algebras over an arbitrary base field.

Frobenius algebra, Non-degenerate bilinear form, Classification, Automorphism

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APA 7 
Asrorov, D.U., Bekbaev, U.D. & Rakhimov, I.S. (2025). Classification of Frobenius algebra structures on two-dimensional vector space over any base field. O‘zbekiston matematika jurnali, 69(4), 22-34.
GOST R 7.0.5 
Asrorov, D.U., Bekbaev, U.D., Rakhimov, I.S. Classification of Frobenius algebra structures on two-dimensional vector space over any base field // O‘zbekiston matematika jurnali. 2025. Т. 69. № 4. С. 22-34.
BibTeX 
@article{d.u.2025,
  author  = {Asrorov, D.U. and Bekbaev, U.D. and Rakhimov, I.S.},
  title   = {Classification of Frobenius algebra structures on two-dimensional vector space over any base field},
  journal = {O‘zbekiston matematika jurnali},
  year    = {2025},
  volume  = {69},
  number  = {4},
  pages   = {22-34}
}
RIS 
TY  - JOUR
AU  - Asrorov, D.U.
AU  - Bekbaev, U.D.
AU  - Rakhimov, I.S.
TI  - Classification of Frobenius algebra structures on two-dimensional vector space over any base field
JO  - O‘zbekiston matematika jurnali
PY  - 2025
VL  - 69
IS  - 4
SP  - 22
EP  - 34
ER  -