Year: 2025
Type: article
Abstract: For an infinite cochain 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 with 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 with 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.
Source: Journal of Mathematical Sciences
Author: A. Zuevsky
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,490
Funder: Akademie Věd České Republiky
Awards: G1741043573, G3967893287
OpenAlex ID: W4411501980