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

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

2007-03-14

arxiv.org/abs/math/0703404v1

International Mathematics Research Notices, Volume 2006, Article ID 97193

Mathematics

Algebraic Topology

16 pages

Scientific paper

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.

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