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Hopf algebras have proved to be very interesting structures with
deep connections to various areas of mathematics, particularly
through quantum groups. Indeed, the study of Hopf algebras, their
representations, their generalizations, and the categories related
to all these objects has an interdisciplinary nature. It finds
methods, relationships, motivations and applications throughout
algebra, category theory, topology, geometry, quantum field theory,
quantum gravity, and also combinatorics, logic, and theoretical
computer science. This volume portrays the vitality of contemporary
research in Hopf algebras. Altogether, the articles in the volume
explore essential aspects of Hopf algebras and some of their
best-known generalizations by means of a variety of approaches and
perspectives. They make use of quite different techniques that are
already consolidated in the area of quantum algebra. This volume
demonstrates the diversity and richness of its subject. Most of its
papers introduce the reader to their respective contexts and
structures through very expository preliminary sections.
The book provides a detailed account of basic coalgebra and Hopf
algebra theory with emphasis on Hopf algebras which are pointed,
semisimple, quasitriangular, or are of certain other quantum
groups. It is intended to be a graduate text as well as a research
monograph.
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