A characteristic map for compact quantum groups

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2016-06-23 DOI:10.1007/s40062-016-0138-y

Atabey Kaygun, Serkan Sütlü

引用次数: 1

Abstract

We show that if G is a compact Lie group and \(\mathfrak {g}\) is its Lie algebra, then there is a map from the Hopf-cyclic cohomology of the quantum enveloping algebra \(U_q(\mathfrak {g})\) to the twisted cyclic cohomology of quantum group algebra \({\mathcal O}(G_q)\). We also show that the Schmüdgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podle? sphere \({\mathcal O}(S^2_q)\) is in the image of this map.

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紧量子群的特征映射

我们证明了如果G是紧李群，\(\mathfrak {g}\)是它的李代数，则存在量子包络代数\(U_q(\mathfrak {g})\)的hopf -环上同调到量子群代数\({\mathcal O}(G_q)\)的扭转环上同调的映射。我们还证明了schm dgen- wagner指数循环与标准Podle?球体\({\mathcal O}(S^2_q)\)在这张地图的图像中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.