Computation of cohomology of Lie conformal and Poisson vertex algebras

• Bojko Bakalov ^[1] ; Alberto De Sole ^[2] ; Victor G. Kac ^[3]
  1. [1] North Carolina State University

     North Carolina State University

     Township of Raleigh, Estados Unidos

     
  2. [2] Sapienza Università di Roma, Italia
  3. [3] MIT, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 4, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00578-2
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• Resumen

  • 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.