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Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras semisimple and non-semisimple , as well as what is known about the extension theory of Hopf algebras.
Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields. Selected pages Title Page. Table of Contents.
Contents Pointed Hopf Algebras. Nichols Algebras. Types of Nichols Algebras. Nichols Algebras of Cartan Type.
Pointed Hopf Algebras of Type An. Coideal Subalgebras and Quantum Symmetric Pairs.
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