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arXiv · 2301.11770

Construction of some non-associative algebras from Associative Algebras with an endomorphism operator, a differential operator or a left averaging operator

Wilson Arley Martinez·Samin Ingrith Ceron
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Abstract

In this paper, we introduce the concepts of endomorphism operator, left averaging operator, differential operator and Rota-Baxter Operator, and we construct examples of these linear maps on associative algebras with a left identity, a skew-idempotent or an idempotent element. These maps on associative algebra induce a non-associative algebra structure such as Lie algebra, Pre-Lie algebra, Jordan algebra, Flexible Algebra or (left) Leibniz algebra. We consider the construction of non-associative algebras from associative algebras with Linear Operators as the main results of this work. In this paper we give examples of non-associative algebras on subspaces of square matrices M3(R).

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Wilson Arley Martinez, Samin Ingrith Ceron. 2023-01-27. Construction of some non-associative algebras from Associative Algebras with an endomorphism operator, a differential operator or a left averaging operator. https://arxiv.org/abs/2301.11770

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