Journal
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY
Volume 56, Issue 1, Pages 175-198Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s13366-013-0157-3
Keywords
Deformation quantization; Invariant differential operators; Lie algebras
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Let G be a connected and simply connected Lie group with Lie algebra g of finite dimension. Let h subset of g be a subalgebra, lambda a character of h, rho the trace of the adjoint representation and epsilon a formal parameter. We prove that the reduction algebra H-0(h(perpendicular to), lambda, q, epsilon) of Cattaneo-Felder for the Poisson manifold g* and the coisotropic submanifold -lambda + h(perpendicular to) is isomorphic with the algebra U(g, h, lambda + rho, epsilon)(h) of ad h-invariant differential operators on G/H. At the last section we prove further results relating various deformations and specializations at epsilon = 1 of these algebras.
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