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Representation Theory
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
Email: khovanov@math.columbia.edu

Aaron D. Lauda
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: lauda@math.columbia.edu

DOI: http://dx.doi.org/10.1090/S1088-4165-09-00346-X
PII: S 1088-4165(09)00346-X
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.