Infinite iterated crossed products of Hopf Algebras, Drinfeld doubles and planar algebras

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Infinite iterated crossed products of Hopf Algebras, Drinfeld doubles and planar algebras

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Title: Infinite iterated crossed products of Hopf Algebras, Drinfeld doubles and planar algebras
Author: Sandipan De
Advisor: Vijay Kodiyalam
Degree: Ph.D
Main Subjects: Mathematics
Institution: HBNI
Year: 2016
Pages: 75p.
Abstract: This thesis deals with the mathematical objects known as planar algebras and their connection with Hopf algebras and their Drinfeld doubles. The motivation for this thesis comes from a series of talks delivered by Prof. Masaki Izumi at IMSc., Chennai, during one of which he asserted that for a Kac algebra subfactor, a related subfactor to its asymptotic inclusion comes from an outer action of its Drinfeld double. This is a folklore result in subfactor theory and in the process of trying to prove this, we noticed a purely algebraic result which also seemed quite interesting and this is one of the main results in the thesis. Given a finite dimensional Hopf algebra H over any field, we associate to it a very natural inclusion A ⊆ B of infinite iterated crossed product algebras. The thesis is divided into four chapters. Chapters 1 and 2 are devoted to a discussion of preliminary notions, namely, Hopf algebras and planar algebras, while the main content of the thesis is contained in Chapters 3 and 4.
URI: http://hdl.handle.net/123456789/378

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