The simplest cohomological invariants for vertex algebras

JOURNAL OF GEOMETRY AND PHYSICS

卷:168

Article

Zuevsky, A.¹ 

[1] Czech Acad Sci, Inst Math, Zitna 25, Prague 11567, Czech Republic

关键词: Vertex algebras;    Cohomological invariants;    Cohomology classes;   

DOI  :  10.1016/j.geomphys.2021.104306

来源: Elsevier

【 摘 要 】

For the double complex structure of grading-restricted vertex algebra cohomology defined in [6,7], 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 simplest 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. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free