Quantum Symmetries in Noncommutative Geometry

Date of Submission

March 2020

Date of Award

3-1-2021

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Statistics

Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

Supervisor

Goswami, Debashish (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

In this thesis, we study quantum symmetries within the realm of noncommutative geometry. These symmetries are captured in two levels of generality, namely, Hopf algebras (or compact quantum groups) in the context of noncommutative differential geometry a la Connes and Hopf algebroids in the context of noncommutative Kaehler geometry a la Ó Buachalla. We compute the orientation-preserving quantum isometry group of the Chakraborty-Pal spectral triple on the odd sphere. Generalizing the Hopf algebra case, we build a framework to take into account Hopf algebroid equivariance in non-commutative complex geometry. We classify complex structures on a canonical spectral triple over the three-point space and identify a universal Hopf algebroid acting on a finite space

Comments

ProQuest Collection ID: https://www.proquest.com/pqdtlocal1010185/dissertations/fromDatabasesLayer?accountid=27563

Control Number

ISILib-TH475

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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