Categorification and higher representation theory
著者
書誌事項
Categorification and higher representation theory
（Contemporary mathematics, 683）
American Mathematical Society, c2017
- タイトル別名
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Categorification
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
I. Losev, Rational Cherednik algebras and categorification
O. Dudas, M. Varagnolo, and E. Vasserot, Categorical actions on unipotent representations of finite classical groups
J. 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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