Mixed graded structure on Chevalley-Eilenberg functors

Abstract

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 $\mathbb{k}$ 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.

Added some more explicit and motivational descriptions of mixed graded complex in the introduction. Second chapter of my PhD thesis, 57 pages, comments welcome

References in corpus (2)

• Algebraic foliations and derived geometry II: the Grothendieck-Riemann-Roch theorem
• A $t$-structure on the $\infty$-category of mixed graded modules