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arXiv · 1010.4696

Cohomology rings for quantized enveloping algebras

Christopher M. Drupieski
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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 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 $\epsilon \in \mathbb{C}$.

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BibTeXRIS

Christopher M. Drupieski. 2010-10-22. Cohomology rings for quantized enveloping algebras. https://doi.org/10.1090/s0002-9939-2013-11659-x

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