Derivation algebra and automorphism group of generalized topological N = 2 superconformal algebra

Yang, Huihui; Yu, Yi; Yao, Tingfu

doi:10.1007/s11464-013-0306-x

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First Cohomology1

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“…See also e.g. Jiang [23], Shen and Jiang [32] and Fu and Gao [13] for related work on other infinite-dimensional Lie algebras, as well as Yang and Yu and Yao [36], and Fa and Han and Yue [5]. Nonetheless, we will provide an explicit algebraic proof of H 1 (W, W) = {0} in the appendix in order to illustrate our techniques.…”

Section: First Cohomologymentioning

confidence: 99%

The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra

Ecker

Schlichenmaier

2019

J. Phys.: Conf. Ser.

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The main aim of this article is to prove the one-dimensionality of the third algebraic cohomology of the Virasoro algebra with values in the adjoint module. We announced this result in a previous publication with only a sketch of the proof. The detailed proof is provided in the present article. We also show that the third algebraic cohomology of the Witt and the Virasoro algebra with values in the trivial module is one-dimensional. We consider purely algebraic cohomology, i.e. our results are independent of any topology chosen. The vanishing of the third algebraic cohomology of the Witt algebra with values in the adjoint module has already been proven by Ecker and Schlichenmaier.

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