Cohomology rings for quantized enveloping algebras (Q2846901)
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scientific article; zbMATH DE number 6204544
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cohomology rings for quantized enveloping algebras |
scientific article; zbMATH DE number 6204544 |
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Cohomology rings for quantized enveloping algebras (English)
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4 September 2013
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quantum group
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enveloping algebra
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cohomology
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exterior algebra
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homogeneous element
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degree
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0.9413141
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0.9311664
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0.9310848
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0.92119575
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0.92066133
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0.9175276
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0.9173896
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The author shows that the cohomology ring for the quantized enveloping algebra associated to a finite dimensional simple complex Lie algebra is generated, as an exterior algebra, by homogeneous elements in the same odd degrees as for generators of the cohomology ring for the original Lie algebra. The author also obtains some partial results for the cohomology rings of non-restricted quantum groups obtained by specializing the quantization parameter to any non-zero complex number. In particular, for transcendental elements and some roots of unity it is shown that degrees of generators again agree with the original Lie algebra.
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