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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Funding
A. P. Pozhidaev was supported by the FAPESP (2018/05372–7) and I. P. Shestakov by the FAPESP (2018/23690–6) and CNPq 304313/2019–0. The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314–2019–0001).
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Pozhidaev, A.P., Shestakov, I.P. On the Right-Symmetric Algebras with a Unital Matrix Subalgebra. Sib Math J 62, 138–147 (2021). https://doi.org/10.1134/S0037446621010158
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DOI: https://doi.org/10.1134/S0037446621010158