The simplest cohomological invariants for vertex algebras

0543309 - MÚ 2022 RIV NL eng J - Článek v odborném periodiku
Zuevsky, Alexander
The simplest cohomological invariants for vertex algebras.
Journal of Geometry and Physics. Roč. 168, October (2021), č. článku 104306. ISSN 0393-0440. E-ISSN 1879-1662
Grant CEP: GA ČR(CZ) GA18-00496S
Institucionální podpora: RVO:67985840
Klíčová slova: vertex algebras * cohomological invariants * cohomology classes
Obor OECD: Pure mathematics
Impakt faktor: 1.380, rok: 2021
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.geomphys.2021.104306

For the double complex structure of grading-restricted vertex algebra cohomology defined in cite{Huang}, we introduce a multiplication of elements of double complex spaces. We show that the orthogonality and bi-grading conditions applied on double complex spaces, provide in relation among mappings and actions of co-boundary operators. Thus, we endow the double complex spaces with structure of bi-graded differential algebra. We then introduce the simples cohomology classes for a grading-restricted vertex algebra, and show their independence on the choice of mappings from double complex spaces. We prove that its cohomology class does not depend on mappings representing of the double complex spaces. Finally, we show that the orthogonality relations together with the bi-grading condition bring about generators and commutation relations for a continual Lie algebra.
Trvalý link: http://hdl.handle.net/11104/0320538