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arXiv · 2609.04805

Derived Associative Algebras and Cyclic Cohomology of Q-manifolds

Andrew James Bruce
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Abstract

Loday's derived product is revisited in the setting of Q-manifolds, i.e., supermanifolds equipped with an odd vector field that `squares to zero'. We interpret the Grassmann odd product as a standard product upon shifting the grading, which implies the existence of a derived (noncommutative) associative $\mathbb{Z}_2$-graded algebra associated with any Q-manifold. We apply Connes' cyclic cohomology to the derived associative algebra, giving a new cohomology on Q-manifolds distinct from the standard cohomology: we refer to this as the derived cyclic cohomology of a Q-manifold. The derived cyclic cocycles are interpreted as classically BRST-invariant functionals within the BV--BFV--BRST formalism or generalised Ruelle--Sullivan currents when applied to regular foliations via their foliation Lie algebroids.

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BibTeXRIS

Andrew James Bruce. 2026-09-04. Derived Associative Algebras and Cyclic Cohomology of Q-manifolds. https://arxiv.org/abs/2609.04805

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