First and Second Cohomologies of Grading-Restricted Vertex Algebras

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Let V be a grading-restricted vertex algebra and W a V-module. We show that for any m ∈ ℤ+, the first cohomology H1m(V, W) of V with coefficients in W introduced by the author is linearly isomorphic to the space of derivations from V to W. In particular, H1m(V, W) for m ∈ ℕ are equal (and can be denoted using the same notation H 1(V, W)). We also show that the second cohomology H21/2(V, W) of V with coefficients in W introduced by the author corresponds bijectively to the set of equivalence classes of square-zero extensions of V by W. In the case that W = V, we show that the second cohomology H21/2(V, V) corresponds bijectively to the set of equivalence classes of first order deformations of V.

Original languageEnglish (US)
Pages (from-to)261-278
Number of pages18
JournalCommunications In Mathematical Physics
Volume327
Issue number1
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'First and Second Cohomologies of Grading-Restricted Vertex Algebras'. Together they form a unique fingerprint.

  • Cite this