TY - JOUR

T1 - On the Hochschild Cohomologies of Associative Conformal Algebras with a Finite Faithful Representation

AU - Kolesnikov, P. S.

AU - Kozlov, R. A.

N1 - Publisher Copyright: © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - IRREDUCIBLE REPRESENTATIONS

UR - http://www.scopus.com/inward/record.url?scp=85060798672&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03309-7

DO - 10.1007/s00220-019-03309-7

M3 - Article

AN - SCOPUS:85060798672

VL - 369

SP - 351

EP - 370

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -