Mixed graded structure on Chevalley-Eilenberg functors
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916663245406208 |
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| author | Pavia, Emanuele |
| author_facet | Pavia, Emanuele |
| contents | In this paper, we shall provide a purely $\infty$-categorical construction of the mixed graded structure over Chevalley-Eilenberg complexes computing homology and cohomology of Lie algebras defined over a field $\Bbbk$ of characteristic $0$. While this additional piece of structure on Chevalley-Eilenberg complexes is expected, and already described in terms of explicit models given by chain complexes, there is not a completely formal and model independent description of the mixed graded Chevalley-Eilenberg $\infty$-functors in available literature. After constructing in all details the Chevalley-Eilenberg $\infty$-functors and studying their main formal properties, we present some further conjectures on their behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_12012 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mixed graded structure on Chevalley-Eilenberg functors Pavia, Emanuele Algebraic Geometry Category Theory K-Theory and Homology In this paper, we shall provide a purely $\infty$-categorical construction of the mixed graded structure over Chevalley-Eilenberg complexes computing homology and cohomology of Lie algebras defined over a field $\Bbbk$ of characteristic $0$. While this additional piece of structure on Chevalley-Eilenberg complexes is expected, and already described in terms of explicit models given by chain complexes, there is not a completely formal and model independent description of the mixed graded Chevalley-Eilenberg $\infty$-functors in available literature. After constructing in all details the Chevalley-Eilenberg $\infty$-functors and studying their main formal properties, we present some further conjectures on their behavior. |
| title | Mixed graded structure on Chevalley-Eilenberg functors |
| topic | Algebraic Geometry Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2207.12012 |