Derived Associative Algebras and Cyclic Cohomology of Q-manifolds

@misc{bruce2026derived,
  title = {{Derived Associative Algebras and Cyclic Cohomology of Q-manifolds}},
  author = {Andrew James Bruce},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04805},
  eprint = {2609.04805},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04805},
}

TY  - UNPB
TI  - Derived Associative Algebras and Cyclic Cohomology of Q-manifolds
AU  - Andrew James Bruce
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.04805
UR  - https://arxiv.org/abs/2609.04805
AB  - 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 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.
ER  -