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Computation of cohomology of Lie conformal and Poisson vertex algebras

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Abstract

We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex algebras. We establish finite dimensionality of this cohomology for conformal Poisson vertex (super)algebras that are finitely and freely generated by elements of positive conformal weight.

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Acknowledgements

This research was partially conducted during the authors’ visits to the University of Rome La Sapienza and to MIT. The first author was supported in part by a Simons Foundation Grant 584741. The second author was partially supported by the national PRIN Fund N. 2015ZWST2C_001 and the University Funds N. RM116154CB35DFD3 and RM11715C7FB74D63. All three authors were supported in part by the Bert and Ann Kostant fund.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Bojko Bakalov

  2. Dipartimento di Matematica, Sapienza Università di Roma, P.le Aldo Moro 2, 00185, Rome, Italy

    Alberto De Sole

  3. Department of Mathematics, MIT, 77 Massachusetts Ave., Cambridge, MA, 02139, USA

    Victor G. Kac

Authors
  1. Bojko Bakalov
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  2. Alberto De Sole
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  3. Victor G. Kac
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Correspondence to Alberto De Sole.

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Bakalov, B., De Sole, A. & Kac, V.G. Computation of cohomology of Lie conformal and Poisson vertex algebras. Sel. Math. New Ser. 26, 50 (2020). https://doi.org/10.1007/s00029-020-00578-2

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  • DOI: https://doi.org/10.1007/s00029-020-00578-2

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