On the Hochschild Cohomologies of Associative Conformal Algebras with a Finite Faithful Representation

P. S. Kolesnikov, R. A. Kozlov

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Abstract

Associative conformal algebras of conformal endomorphisms are of essential importance for the study of finite representations of conformal Lie algebras (Lie vertex algebras). We describe all semisimple algebras of conformal endomorphisms which have the trivial second Hochschild cohomology group with coefficients in every conformal bimodule. As a consequence, we state a complete solution of the radical splitting problem in the class of associative conformal algebras with a finite faithful representation.

Original languageEnglish
Pages (from-to)351-370
Number of pages20
JournalCommunications in Mathematical Physics
Volume369
Issue number1
DOIs
Publication statusPublished - 1 Jul 2019

Keywords

  • IRREDUCIBLE REPRESENTATIONS

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