Huang, YZ (reprint author), Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA.
部门归属:
[Huang, Yi-Zhi] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China; [Huang, Yi-Zhi] Chinese Acad Sci, Kavali Inst Theoret Phys China, Beijing 100190, Peoples R China
英文摘要:
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.
