1. The isomorphism problem in the context of PI-theory for two-dimensional Jordan algebras.
- Author
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Diniz, Diogo, Gonçalves, Dimas José, da Silva, Viviane Ribeiro Tomaz, and Souza, Manuela da Silva
- Subjects
- *
JORDAN algebras , *FINITE fields , *GROBNER bases , *ISOMORPHISM (Mathematics) , *POLYNOMIALS , *ALGEBRA - Abstract
Let F be a field of characteristic different from 2. Small-dimensional Jordan algebras over F have been extensively studied and classified. In the present paper we show that any two-dimensional Jordan algebras over a finite field are isomorphic if and only if they satisfy the same polynomial identities (the opposite happens in the case F is infinite, even if algebraically closed). We determine a finite generating set for the T-ideal of the polynomial identities of every two-dimensional Jordan algebra when F is finite, and linear bases for the corresponding relatively free algebras are also determined. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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