Non-Commutative Geometry: Hopf Algebras and Quantum Groups

Saha, Abhigyan (2021) Non-Commutative Geometry: Hopf Algebras and Quantum Groups. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Abhigyan Saha (16MS166)) 16MS166_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

The goal of this project is to get an introductory understanding of the vast field of Non-Commutative Geometry, in this case, with emphasis on Hopf Algebras and Quantum Groups. We present some important results from Representation Theory of Finite Groups in the first chapter, moving on to the structures of Algebras and the analogous representation theory in the second chapter. We study the naturally consequent topics of Co-algebras and Bi-algebras, followed by the addition of an “antipode” map in the third chapter, and the resulting Hopf Algebra structure. One of the main Theorems in this section deals with the existence of semi-simple Hopf Algebras under certain conditions. The final chapter is my foray into the study of Quantum Groups, which I shall be continuing with in subsequent projects.

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