Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres
نویسندگان
چکیده
منابع مشابه
Regularity and dimension spectrum of the equivariant spectral triple for the odd dimensional quantum spheres
The odd dimensional quantum sphere S q is a homogeneous space for the quantum group SUq(l + 1). A generic equivariant spectral triple for S 2l+1 q on its L2 space was constructed by Chakraborty & Pal in [4]. We prove regularity for that spectral triple here. We also compute its dimension spectrum and show that it is simple. We give detailed construction of its smooth function algebra and some r...
متن کاملq-FUZZY SPHERES AND QUANTUM DIFFERENTIALS ON Bq[SU2] AND Uq(su2)
We show that the 2-parameter Podles sphere is a q-fuzzy sphere precisely interpolating between the fuzzy sphere as quotient of the angular momentum algebra U(su2) and the standard q-sphere Cq [S] as subalgebra of the quantum group Cq [SU2]. Whereas the classical sphere as CP 1 can be defined as the algebra generated by the matrix entries of a projector e with trace(e) = 1, the fuzzy-sphere is d...
متن کاملCharacterization of SUq(l + 1)-equivariant spectral triples for the odd dimensional quantum spheres
Abstract The quantum group SUq(l + 1) has a canonical action on the odd dimensional sphere S q . All odd spectral triples acting on the L2 space of S 2l+1 q and equivariant under this action have been characterized. This characterization then leads to the construction of an optimum family of equivariant spectral triples having nontrivial K-homology class. These generalize the results of Chakrab...
متن کاملEquivariant spectral triples for SUq(l + 1) and the odd dimensional quantum spheres
We formulate the notion of equivariance of an operator with respect to a covariant representation of a C∗-dynamical system. We then use a combinatorial technique used by the authors earlier in characterizing spectral triples for SUq(2) to investigate equivariant spectral triples for two classes of spaces: the quantum groups SUq(l+1) for l > 1, and the odd dimensional quantum spheres S q of Vaks...
متن کاملEquivariant spectral triples on the quantum SU(2) group
We characterize all equivariant odd spectral triples on the quantum SU(2) group having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and there does exist a 3-summable equivariant spectral triple. We also show that given any odd spectral triple, there is an odd equivariant spectral triple that induces the same element in K. AMS ...
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: Banach Center Publications
سال: 2011
ISSN: 0137-6934,1730-6299
DOI: 10.4064/bc93-0-18