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Representation Theory

ISSN 1088-4165



A diagrammatic approach to categorification of quantum groups I

Authors: Mikhail Khovanov and Aaron D. Lauda
Journal: Represent. Theory 13 (2009), 309-347
MSC (2000): Primary 81R50, 16S99
Published electronically: July 28, 2009
MathSciNet review: 2525917
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Abstract: To each graph without loops and multiple edges we assign a family of rings. Categories of projective modules over these rings categorify $U^-_q(\mathfrak {g})$, where $\mathfrak {g}$ is the Kac-Moody Lie algebra associated with the graph.

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Additional Information

Mikhail Khovanov
Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Address at time of publication: Department of Mathematics, Columbia University, New York, New York 10027
MR Author ID: 363306

Aaron D. Lauda
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
ORCID: setImmediate$0.06573403963950497$1

Keywords: Categorification, quantum groups, Grothendieck ring, canonical basis
Received by editor(s): August 7, 2008
Published electronically: July 28, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.