The Geometry of some Quantum Homogeneous Spaces and the Weak Heat Kernel Expansion[HBNI Th 29]

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The Geometry of some Quantum Homogeneous Spaces and the Weak Heat Kernel Expansion[HBNI Th 29]

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dc.contributor.author Sundar, S
dc.date.accessioned 2011-08-24T07:23:19Z
dc.date.available 2011-08-24T07:23:19Z
dc.date.issued 2011-08-24T07:23:19Z
dc.date.submitted 2011
dc.identifier.uri http://hdl.handle.net/123456789/253
dc.description.abstract We study the non-commutative geometry of some quantum homogeneous spaces associated with the quantum group SUq(n). First we consider the quantum space SUq(n)/SUq(n − 1) called the odd dimensional quantum spheres and denoted S2n−1 q . We consider two spectral triples associated to the odd dimensional quantum spheres S2n−1 q . We show that the spectral triples satisfy the hypothesis of the local index formula. A conceptual explanation is given by considering a property which we call the weak heat kernel asymptotic expansion property of spectral triples. We show that a spectral triple having the weak heat kernel asymptotic expansion property satisfies the hypothesis of the local index formula. We also show that this property is stable under quantum double suspension. Finally we compute the K-groups of the quantum homogeneous space SUq(n)/SUq(n − 2). en_US
dc.publisher.publisher
dc.relation.isbasedon • ArupKumar Pal and S.Sundar. Regularity and dimension spectrum of the equivariant spectral triple for the odd dimensional quantum spheres, Journal of Noncommutative Geometry, 389-439, Vol 4, Issue 3, 2010 • Partha Sarathi Chakraborty and S.Sundar. Quantum double suspension and spectral triples, Journal of functional analysis, 2011, doi:10.1016/j.jfa.2011.01.009 • Partha Sarathi Chakraborty and S.Sundar. K-groups of the quantum homogeneous space SUq(n)/SUq(n − 2). arXiv:1006.1742/math.KT en_US
dc.subject Quantum Spaces en_US
dc.subject Heat Kernel Expansion en_US
dc.subject HBNI Th 29 en_US
dc.title The Geometry of some Quantum Homogeneous Spaces and the Weak Heat Kernel Expansion[HBNI Th 29] en_US
dc.type.degree Ph.D en_US
dc.type.institution HBNI en_US
dc.description.advisor Partha Sarathi Chakraborty
dc.type.mainsub Mathematics en_US

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