Construction of some non-associative algebras from Associative Algebras with an endomorphism operator, a differential operator or a left averaging operator
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909112760008704 |
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| author | Martinez, Wilson Arley Ceron, Samin Ingrith |
| author_facet | Martinez, Wilson Arley Ceron, Samin Ingrith |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11770 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Construction of some non-associative algebras from Associative Algebras with an endomorphism operator, a differential operator or a left averaging operator Martinez, Wilson Arley Ceron, Samin Ingrith Rings and Algebras 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). |
| title | Construction of some non-associative algebras from Associative Algebras with an endomorphism operator, a differential operator or a left averaging operator |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2301.11770 |