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 1970s 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.
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