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Poisson Vertex Algebra Cohomology and Differential Harrison Cohomology

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Representation Theory, Mathematical Physics, and Integrable Systems

Part of the book series: Progress in Mathematics ((PM,volume 340))

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Abstract

We construct a canonical map from the Poisson vertex algebra cohomology complex to the differential Harrison cohomology complex, which restricts to an isomorphism on the top degree. This is an important step in the computation of Poisson vertex algebra and vertex algebra cohomologies.

To Nikolai Reshetikhin on his 60-th birthday.

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References

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Acknowledgements

This research was partially conducted during the authors’ visits to the University of Rome La Sapienza, to MIT, and to IHES. 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. The third author was partially supported by the Bert and Ann Kostant fund and by a Simons Fellowship.

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Authors and Affiliations

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

    Bojko Bakalov

  2. Dipartimento di Matematica, Sapienza Università di Roma, Rome, Italy

    Alberto De Sole & Veronica Vignoli

  3. Department of Mathematics, MIT, Cambridge, MA, 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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  4. Veronica Vignoli
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Corresponding author

Correspondence to Victor G. Kac .

Editor information

Editors and Affiliations

  1. Section de Mathématiques, Université de Genève, Genève 4, Switzerland

    Anton Alekseev

  2. Department of Mathematics, University of California at Berkley, Berkeley, CA, USA

    Edward Frenkel

  3. Mathematics Department, Institut de Mathématiques de Jussieu, Paris Cedex 13, France

    Marc Rosso

  4. Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada

    Ben Webster

  5. Department of Mathematics, Northeastern University, Boston, MA, USA

    Milen Yakimov

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Bakalov, B., Sole, A.D., Kac, V.G., Vignoli, V. (2021). Poisson Vertex Algebra Cohomology and Differential Harrison Cohomology. In: Alekseev, A., Frenkel, E., Rosso, M., Webster, B., Yakimov, M. (eds) Representation Theory, Mathematical Physics, and Integrable Systems. Progress in Mathematics, vol 340. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-78148-4_2

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