Beck modules and alternative algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915074466119680 |
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| author | Dhankhar, Nishant Miller, Haynes Tahboub, Ali Yin, Victor |
| author_facet | Dhankhar, Nishant Miller, Haynes Tahboub, Ali Yin, Victor |
| contents | We set out the general theory of ``Beck modules'' in a variety of algebras and describe them as modules over suitable ``universal enveloping'' unital associative algebras. We develop a theory of ``noncommutative partial differentiation'' to pass from the equations of the variety to relations in a universal enveloping algebra. We pay particular attention to the case of alternative algebras, defined by a restricted associative law, and determine the Poincaré polynomial of the universal enveloping algebra in the homogeneous case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07962 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Beck modules and alternative algebras Dhankhar, Nishant Miller, Haynes Tahboub, Ali Yin, Victor Rings and Algebras 17A30, 17.04 We set out the general theory of ``Beck modules'' in a variety of algebras and describe them as modules over suitable ``universal enveloping'' unital associative algebras. We develop a theory of ``noncommutative partial differentiation'' to pass from the equations of the variety to relations in a universal enveloping algebra. We pay particular attention to the case of alternative algebras, defined by a restricted associative law, and determine the Poincaré polynomial of the universal enveloping algebra in the homogeneous case. |
| title | Beck modules and alternative algebras |
| topic | Rings and Algebras 17A30, 17.04 |
| url | https://arxiv.org/abs/2309.07962 |