dorsal/arxiv
View SchemaSemiinfinite cohomology of quantum groups II
| Authors | Sergey Arkhipov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9610020 |
| URL | https://arxiv.org/abs/q-alg/9610020 |
Abstract
It is known that the semi-infinite cohomology spaces of the infinitely twisted nilpotent subalgebra in an affine Lie algebra $g$ with coefficients in an integrable simple module over the affine Lie algebra have a base enumerated by elements of the corresponding affine Weyl group graded by the semiinfinite length function. Let $U$ be the affine quantum group corresponding to $g$. It is possible to define a subalgebra in $U$ being the quantum analogue of the universal enveloping algebra of the infinitely twisted nilpotent subalgebra in $g$. In this paper we prove that for general values of the parameter $v$ the semiinfinite cohomology of this associative algebra with coefficients in an integrable simple module over $U$ coincides with the one of the corresponding Lie subalgebra in $g$ with coefficients in the corresponding $g$-module.
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"abstract": "It is known that the semi-infinite cohomology spaces of the infinitely\ntwisted nilpotent subalgebra in an affine Lie algebra $g$ with coefficients in\nan integrable simple module over the affine Lie algebra have a base enumerated\nby elements of the corresponding affine Weyl group graded by the semiinfinite\nlength function. Let $U$ be the affine quantum group corresponding to $g$. It\nis possible to define a subalgebra in $U$ being the quantum analogue of the\nuniversal enveloping algebra of the infinitely twisted nilpotent subalgebra in\n$g$. In this paper we prove that for general values of the parameter $v$ the\nsemiinfinite cohomology of this associative algebra with coefficients in an\nintegrable simple module over $U$ coincides with the one of the corresponding\nLie subalgebra in $g$ with coefficients in the corresponding $g$-module.",
"arxiv_id": "q-alg/9610020",
"authors": [
"Sergey Arkhipov"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Semiinfinite cohomology of quantum groups II",
"url": "https://arxiv.org/abs/q-alg/9610020"
},
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