Bigraded differential algebra for vertex algebra complexes
Abstract
For an infinite chain bicomplex we show that the orthogonality and grading conditions provide it with the structure of a bigraded differential algebra with respect to a natural multiplication of several elements bicomplex spaces. Corresponding bigraded algebra commutation relations generate a sequence of non-vanishing cohomology invariants associated to vertex algebras. In particular, we apply this result to the bicomplex of grading-restricted vertex algebra cohomology endowed with a multiplication we introduce. We provide examples associated to various choices of vertex algebra bicomplex subspaces. The generators and commutation relations of the bigraded differential algebra form a continual Lie algebra with the root space provided by a grading-restricted vertex algebra.
Cite
@article{arxiv.2106.06014,
title = {Bigraded differential algebra for vertex algebra complexes},
author = {A. Zuevsky},
journal= {arXiv preprint arXiv:2106.06014},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2012.07343, arXiv:2012.05904; text overlap with arXiv:1006.2516 by other authors