ebook9783319979878d4325

Description

This textbook presents the second edition of Manin’s celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others.¬† This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin’s lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka‚ÄìKrein formalism, which further strengthens Manin’s approach to symmetry and moduli-objects in noncommutative geometry.