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Baum-Connes conjecture, flag varieties and representations of semisimple Lie groups.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Wei, Zhaoting.
- Language:
- English
- Subjects (All):
- Mathematics.
- Applied mathematics.
- 0364.
- 0405.
- Penn dissertations--Mathematics.
- Mathematics--Penn dissertations.
- Local Subjects:
- Penn dissertations--Mathematics.
- Mathematics--Penn dissertations.
- 0364.
- 0405.
- Physical Description:
- 94 pages
- Contained In:
- Dissertation Abstracts International 74-10B(E).
- System Details:
- Mode of access: World Wide Web.
- text file
- Summary:
- This thesis consists of three chapters. In Chapter 1 we review the Baum-Connes conjecture and its relation with representation theory In Chapter 2 we describe the equivariant K-theory of the real semisimple Lie group which acts on the (complex) flag variety of its complexification group. We construct an assembly map in the framework of KK-theory. Then we prove that it is an isomorphism. The prove relies on a careful study of the orbits of the real group action on the flag variety and then piecing together the orbits. This result can be considered as a special case of the Baum-Connes conjecture with coefficient.
- In Chapter 3 we study the noncommutative Poisson bracket P on the classical family algebra. We show that P is the first-order deformation from the classical family algebra to the quantum family algebra. We will prove that the noncommutative Poisson bracket is in fact a Hochschild 2-coboundary therefore the deformation is infinitesimally trivial.
- In the appendix we talk about some further topics and open problems in this area.
- Notes:
- Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2013.
- Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.
- Adviser: Jonathan Block.
- Local Notes:
- School code: 0175.
- ISBN:
- 9781303176692
- Access Restriction:
- Restricted for use by site license.
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