Reference : The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with va...
Scientific congresses, symposiums and conference proceedings : Paper published in a journal
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/41417
The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in natural modules
English
Ecker, Jill Marie-Anne mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Schlichenmaier, Martin mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2020
Banach Center Publications
PWN
Yes
International
0137-6934
1730-6299
Warszawa
Poland
Homotopy algebras, deformation theory and quantization
from 16-09-2018 to 22-09-2018
Bedlewo
Poland
[en] Witt algebra ; Virasoro algebra ; Lie algebra cohomology ; Deformations of algebras ; Conformal field theory
[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.
Researchers
http://hdl.handle.net/10993/41417

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