Generalized Clifford algebras, weighted polynomial laws, and adjunction
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915578786086912 |
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| author | Bach, Nguyen Xuan |
| author_facet | Bach, Nguyen Xuan |
| contents | In this paper, we study Clifford algebra construction from the perspective of adjunctions motivated by the general framework of Krashen and Lieblich. We introduce a category of weighted polynomial laws whose associated Clifford algebra functor is a left adjoint on this category. We introduce a notion of lifting weighted polynomial laws generalizing explicit constructions of Krashen and Lieblich. As another application, we construct derived Clifford algebras of derived homogeneous polynomial forms of arbitrary degree with noncommutative coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Clifford algebras, weighted polynomial laws, and adjunction Bach, Nguyen Xuan Algebraic Geometry Category Theory Rings and Algebras In this paper, we study Clifford algebra construction from the perspective of adjunctions motivated by the general framework of Krashen and Lieblich. We introduce a category of weighted polynomial laws whose associated Clifford algebra functor is a left adjoint on this category. We introduce a notion of lifting weighted polynomial laws generalizing explicit constructions of Krashen and Lieblich. As another application, we construct derived Clifford algebras of derived homogeneous polynomial forms of arbitrary degree with noncommutative coefficients. |
| title | Generalized Clifford algebras, weighted polynomial laws, and adjunction |
| topic | Algebraic Geometry Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2510.06560 |