Cohomology of the Schrödinger-Virasoro conformal algebra

Abstract

Both the basic cohomology groups and the reduced cohomology groups of the Schrödinger-Virasoro conformal algebra with trivial coefficients are completely determined.

Cohomology of the extended Schrödinger-Virasoro conformal algebra

“…Let γ be an arbitrary 3-cocycle. With the similar discussion in Lemma 3.6 in [19], we can assume that…”

“…The general cohomology theory of conformal algebras with coefficients in an arbitrary conformal module was systematically developed in [2]. All cohomology groups of the Virasoro conformal algebra, the Heisenberg-Virasoro conformal algebra and the Schrödinger-Virasoro conformal algebra with trivial coefficients were determined in [2,22,19], respectively. Also, some low dimensional cohomology groups of the general Lie conformal algebras gc N were determined in [15].…”

“…In the present paper, we focus on the cohomology of the extended Schrödinger-Virasoro conformal algebra, denoted by SV and introduced in [17]. By definition, SV is a finite Lie conformal algebra with free generators L, N, Y, M subject to the following nontrivial λ-brackets [4,2,20,22,19], respectively.…”