Abstract: In the present talk we give classification of all finite-dimensional left(right)-symmetric algebras A = W ⊕ M2 over a field F of characteristic zero such that W is an irreducible unital right module over M2 := M2(F), and M2 is a subalgebra of A, whose unity E serves as the unity for A as well (we call such subalgebras unital). We also show that for every natural n there exists a simple nonassociative left(right)-symmetric algebra, which possesses the “unital” matrix subalgebra Mn(F).

Cite: Пожидаев А.П. , Шестаков И.П.
The right-symmetric algebras possessing a “unital” matrix subalgebra
Международная конференция "Мальцевские чтения" 19-23 авг. 2019