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The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in natural modules
Ecker, Jill Marie-Anne; Schlichenmaier, Martin
2021In Banach Center Publications, 123, p. 141-174
Peer reviewed
 

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Keywords :
Witt algebra; Virasoro algebra; Lie algebra cohomology; Deformations of algebras; Conformal field theory
Abstract :
[en] The main aim of this contribution is to compute the low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in the adjoint and the trivial module. The last section includes results for the general tensor densities modules, presented without proof. One of our main results is that the third algebraic cohomology of the Witt algebra with values in the adjoint module vanishes, while it is one-dimensional for the Virasoro algebra. The first and the second algebraic cohomology of the Witt and the Virasoro algebra with values in tensor densities modules vanish for almost all modules. In the case they do not vanish, we give explicit expressions for the generating cocycles. In our work, we consider algebraic cohomology and not only the sub-complex of continuous cohomology, meaning we do not put any continuity constraints on the cochains. Consequently, our results are independent of any choice of an underlying topology, and valid for any concrete realizations of the considered Lie algebras.
Disciplines :
Mathematics
Author, co-author :
Ecker, Jill Marie-Anne ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Schlichenmaier, Martin  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in natural modules
Publication date :
2021
Event name :
Homotopy algebras, deformation theory and quantization
Event place :
Bedlewo, Poland
Event date :
from 16-09-2018 to 22-09-2018
By request :
Yes
Audience :
International
Journal title :
Banach Center Publications
Special issue title :
Homotopy algebras, deformation theory and quantization
Volume :
123
Pages :
141-174
Peer reviewed :
Peer reviewed
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