Cohomology rings for quantized enveloping algebras

Drupieski, Christopher

doi:10.1090/S0002-9939-2013-11659-X

Cohomology rings for quantized enveloping algebras
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by Christopher M. Drupieski

Proc. Amer. Math. Soc. 141 (2013), 3739-3753

DOI: https://doi.org/10.1090/S0002-9939-2013-11659-X

Published electronically: July 16, 2013

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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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