Computation of cohomology of Lie conformal and Poisson vertex algebras

Selecta Mathematica - Tập 26 - Trang 1-51 - 2020
Bojko Bakalov1, Alberto De Sole2, Victor G. Kac3
1Department of Mathematics, North Carolina State University, Raleigh, USA
2Dipartimento di Matematica, Sapienza Università di Roma, Rome, Italy
3Department of Mathematics, MIT, Cambridge, USA

Tóm tắt

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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