480 research outputs found
Traces and Characteristic Classes in Infinite Dimensions
This paper surveys topological results obtained from characteristic classes
built from the two types of traces on the algebra of pseudodifferential
operators of nonpositive order. The main results are the construction of a
universal -polynomial and Chern character that control the -index
theorem for all circle actions on a fixed vector bundle over a manifold, and
, for the diffeomorphism
group of circle bundles with large first Chern class over projective
algebraic Kaehler surfaces.Comment: Parts of Section 2.3 are not correct. This is discussed in T.
McCauley, "S^1-Equivariant Chern-Weil Constructions on Loop Spaces,"
arXiv:1507.0862
Universal Deformation Formulae, Symplectic Lie groups and Symmetric Spaces
We apply methods from strict quantization of solvable symmetric spaces to
obtain universal deformation formulae for actions of a class of solvable Lie
groups. We also study compatible co-products by generalizing the notion of
smash product in the context of Hopf algebras
Universal Deformation Formulae for Three-Dimensional Solvable Lie groups
We apply methods from strict quantization of solvable symmetric spaces to
obtain universal deformation formulae for actions of every three-dimensional
solvable Lie group. We also study compatible co-products by generalizing the
notion of smash product in the context of Hopf algebras. We investigate in
particular the dressing action of the `book' group on SU(2)
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