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Cohomology rings for quantized enveloping algebras


Author: Christopher M. Drupieski
Journal: Proc. Amer. Math. Soc. 141 (2013), 3739-3753
MSC (2010): Primary 17B37, 17B56
DOI: https://doi.org/10.1090/S0002-9939-2013-11659-X
Published electronically: July 16, 2013
MathSciNet review: 3091765
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Abstract: We compute the structure of the cohomology ring for the quantized enveloping algebra (quantum group) $ U_q$ associated to a finite-dimensional simple complex Lie algebra $ \mathfrak{g}$. We show that the cohomology ring is generated as an exterior algebra by homogeneous elements in the same odd degrees as those that generate the cohomology ring for the Lie algebra $ \mathfrak{g}$. Partial results are also obtained for the cohomology rings of the non-restricted quantum groups obtained from $ U_q$ by specializing the parameter $ q$ to a non-zero value $ \varepsilon \in \mathbb{C}$.


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Additional Information

Christopher M. Drupieski
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602-7403
Address at time of publication: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614
Email: cdrup@math.uga.edu, cdrupies@depaul.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11659-X
Received by editor(s): October 21, 2010
Received by editor(s) in revised form: December 23, 2011, and January 18, 2012
Published electronically: July 16, 2013
Additional Notes: The author was supported in part by NSF VIGRE grant DMS-0738586.
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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