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Lectures on Algebraic Categorification
The QGM Master Class Series

Volodymyr Mazorchuk (Uppsala University, Sweden)

Lectures on Algebraic Categorification

ISBN print 978-3-03719-108-8, ISBN online 978-3-03719-608-3
DOI 10.4171/108
March 2012, 128 pages, softcover, 17 x 24 cm.
28.00 Euro

The term “categorification” was introduced by Louis Crane in 1995 and refers to the process of replacing set-theoretic notions by the corresponding category-theoretic analogues.

This text mostly concentrates on algebraical aspects of the theory, presented in the historical perspective, but also contains several topological applications, in particular, an algebraic (or, more precisely, representation-theoretical) approach to categorification. It consists of fifteen sections corresponding to fifteen one-hour lectures given during a Master Class at Aarhus University, Denmark in October 2010. There are some exercises collected at the end of the text and a rather extensive list of references. Video recordings of all (but one) lectures are available from the Master Class website.

The book provides an introductory overview of the subject rather than a fully detailed monograph. Emphasis is on definitions, examples and formulations of the results. Most proofs are either briefly outlined or omitted. However, complete proofs can be found by tracking references. It is assumed that the reader is familiar with the basics of category theory, representation theory, topology and Lie algebra.

Keywords: Categorification, 2-category, Lie algebra, module, category O, functor, knot, Jones polynomial, Verma module, translation functor

Further Information

Review in Zentralblatt MATH 1238.18001

Review in MR 2918217