Quantum symmetric spaces

J. Donin; S. Shnider

doi:10.1016/0022-4049(95)00015-O

Quantum symmetric spaces

J. Donin, S. Shnider

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

Let G be a semisimple Lie group, g its Lie algebra. For any symmetric space M over G we construct a new (deformed) multiplication in the space A of smooth functions on M. This multiplication is invariant under the action of the Drinfeld-Jimbo quantum group U_hg and is commutative with respect to an involutive operator S ̃: A ⊗ A → A ⊗ A. Such a multiplication is unique. Let M be a kählerian symmetric space with the canonical Poisson structure. Then we construct a U_hg-invariant multiplication in A which depends on two parameters and is a quantization of that structure.

Original language	English
Pages (from-to)	103-115
Number of pages	13
Journal	Journal of Pure and Applied Algebra
Volume	100
Issue number	1-3
DOIs	https://doi.org/10.1016/0022-4049(95)00015-O
State	Published - 12 May 1995

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Quantum symmetric spaces

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