First and Second Cohomologies of Grading-Restricted Vertex Algebras

被引：13

作者：

Huang, Yi-Zhi ^{[1
,2
]}

机构：

[1] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

[2] Chinese Acad Sci, Kavali Inst Theoret Phys China, Beijing 100190, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2014年 / 327卷 / 01期

关键词：

Equivalence Class; Vertex Operator; Identity Property; Vertex Operator Algebra; Absolute Convergence;

D O I：

10.1007/s00220-014-1946-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Let V be a grading-restricted vertex algebra and W a V-module. We show that for any , the first cohomology of V with coefficients in W introduced by the author is linearly isomorphic to the space of derivations from V to W. In particular, for are equal (and can be denoted using the same notation H (1)(V, W)). We also show that the second cohomology 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 corresponds bijectively to the set of equivalence classes of first order deformations of V.

引用

页码：261 / 278

页数：18