Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Bruce, Andrew James
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211877424