Quantizations of compact Lie group actions
نویسندگان
چکیده
منابع مشابه
Desingularizing Compact Lie Group Actions
This note surveys the well-known structure of G-manifolds and summarizes parts of two papers that have not yet appeared: [4], joint with J. Brüning and F. W. Kamber, and [8], joint with I. Prokhorenkov. In particular, from a given manifold on which a compact Lie group acts smoothly, we construct a sequence of manifolds on which the same Lie group acts, but with fewer levels of singular strata. ...
متن کاملLie group actions on compact
Let G be a homotopically trivial and effective compact Lie group action on a compact manifold N of nonpositive curvature. Under certain assumptions on N we prove that if G has dimension equal to rank of Center π1(N), then G must be connected. Furthermore, if on N there exists a point having negative definite Ricci tensor, then we show that G is the trivial group.
متن کاملBorsuk-ulam Type Theorems for Compact Lie Group Actions
Borsuk-Ulam type theorems for arbitrary compact Lie group actions are proven. The transfer plays a major role in this approach. We present Borsuk-Ulam type theorems for arbitrary compact Lie group actions. The essence of our approach is a generalization of the ideal-valued index of FadellHusseini [FH88] using transfer [Boa66], [BG75], [Dol76], [KP72], [Rou71]. Once an appropriate concept (Defin...
متن کاملTwisted Lie group C-algebras as strict quantizations
A nonzero 2-cocycle Γ ∈ Z(g,R) on the Lie algebra g of a compact Lie group G defines a twisted version of the Lie-Poisson structure on the dual Lie algebra g∗, leading to a Poisson algebra C∞(g∗(Γ)). Similarly, a multiplier c ∈ Z (G, U(1)) on G which is smooth near the identity defines a twist in the convolution product on G, encoded by the twisted group C∗algebra C∗(G, c). Further to some supe...
متن کاملThe Topology of Compact Lie Group Actions through the Lens of Finite Models
Given a compact, connected Lie group K, we use principal K-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let M be a compact, connected, smooth manifold which supports an almost free K-action. Under a partial formality assumption on the orbit space and a regularity assumption on the characteristic classes of the action, we describe an algebraic m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2014
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2014.01.015