A. P. Pozhidaev, I. P. Shestakov
Abstract
Under study are the right-symmetric algebras over a field $ F $ which possess a “unital” matrix subalgebra $ M_{n}(F) $ . We classify all these finite-dimensional right-symmetric algebras $ {\mathcal{A}}=W\oplus M_{2}(F) $ in the case when $ W $ is an irreducible module over $ sl_{2}(F) $ .
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Under study are the right-symmetric algebras over a field $ F $ which possess a “unital” matrix subalgebra $ M_{n}(F) $ . We classify all these finite-dimensional right-symmetric algebras $ {\mathcal{A}}=W\oplus M_{2}(F) $ in the case when $ W $ is an irreducible module over $ sl_{2}(F) $ .
Key concepts: Unital, Subalgebra, Mathematics, Pure mathematics, Field (mathematics), Matrix (chemical analysis), Combinatorics, Algebra over a field