Derivations, automorphisms and second cohomology of generalized loop Schrödinger-Virasoro algebras

Abstract

The derivation algebras, automorphism groups and second cohomology groups of the generalized loop Schrödinger-Virasoro algebras are completely determined in this paper.

Loop Schrödinger–Virasoro Lie conformal algebra

“…The Schrödinger-Virasoro Lie algebra was introduced in the context of nonequilibrium statistical physics during the process of investigating the free Schrödinger equations in [9]. There are two sectors of this type Lie algebras, i.e., the original one and the twisted one, both of which are closely related to the Schrödinger algebra and the Virasoro algebra, which play important roles in many areas of mathematics and physics and have been investigated in a series of papers (see, e.g., [2,8,12,18]). The (extended) loop Schrödinger-Virasoro algebra is the Lie algebra of the tensor product of the (extended) Schrödinger-Virasoro algebra and the Laurent polynomial algebra.…”