Batalin-Vilkovisky Lie Algebra Structure on the Loop Homology of Complex Stiefel Manifolds

Abstract

We determine the Batalin-Vilkovisky Lie algebra structure for the integral loop homology of special unitary groups and complex Stiefel manifolds. It is shown to coincide with the Poisson algebra structure associated to a certain odd symplectic form on a super vector space for which loop homology is the super algebra of functions. Over rationals, the loop homology of the above spaces splits into a tensor product of simple BV algebras, and it is shown to contain a super Lie algebra.