Morse Matching Method for Conformal Cohomologies

Abstract

Abstract. We apply discrete algebraic Morse theory to the computation of Hochschild cohomologies of associative conformal algebras. As an example, we evaluate the dimensions of the Hochschild cohomology groups with scalar coefficients of the universal associative conformal envelope U(3) of the Virasoro Lie conformal algebra relative to the associative locality bound N = 3 on the generator. In contrast to the Weyl conformal algebra U(2) which is the universal associative conformal envelope of the Virasoro conformal algebra relative to the locality bound N = 2, not all Hochschild cohomologies of U(3) are trivial.

Keywords: Conformal algebras, Hochschild cohomology, Groubner -- Shirshov basis, Morse mathching