New examples of infinite-dimensional n-Lie algebras

Abstract

In this paper we study the second cohomology space for the n-th Schrödinger algebra sch n . We prove that the second cohomology space is vanishing for n ≥ 3 and show that dim(H 2 (sch 2 , sch 2 )) = 2. Moreover, we investigate the factor algebra of the Schrödinger algebra by its center and determine the second cohomology group of this factor algebra.