The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory.This volume exhibits some of the current trends in higher representation theory and the diverse techniques that are being employed in this field with the aim of showcasing the many applications of higher representation theory.The companion volume (Contemporary Mathematics, Volume 684) is devoted to categorification in geometry, topology, and physics.
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Presents some of the current trends in higher representation theory and the diverse techniques that are being employed in this field with the aim of showcasing the many applications of higher representation theory. The companion volume (Contemporary Mathematics, Volume 684) is devoted to categorification in geometry, topology, and physics.
Les mer
I. Losev, Rational Cherednik algebras and categorificationO. Dudas, M. Varagnolo, and E. Vasserot, Categorical actions on unipotent representations of finite classical groupsJ. Brundan and N. Davidson, Categorical actions and crystals A. M. Licata, On the 2-linearity of the free group M. Ehrig, C. Stroppel, and D. Tubbenhauer, The Blanchet-Khovanov algebras G. Lusztig, Generic character sheaves on groups over $k[\epsilon]/(\epsilon^r)$ D. Berdeja Suarez, Integral presentations of quantum lattice Heisenberg algebras Y. Qi and J. Sussan, Categorification at prime roots of unity and hopfological finiteness B. Elias, Folding with Soergel bimodules L. T. Jensen and G. Williamson, The $p$-canonical basis for Hecke algebras.
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Produktdetaljer

ISBN
9781470424602
Publisert
2017-03-30
Utgiver
Vendor
American Mathematical Society
Vekt
530 gr
Høyde
254 mm
Bredde
178 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
363

Biographical note

Anna Beliakova, Universitat Zurich, Switzerland.

Aaron D. Lauda, University of Southern California, Los Angeles, CA.