The set of equivalent classes of invariant star products on ( G ; β 1)
Identifieur interne : 000499 ( Main/Exploration ); précédent : 000498; suivant : 000500The set of equivalent classes of invariant star products on ( G ; β 1)
Auteurs : Carlos Moreno [Espagne, France] ; Luis Valero [Espagne]Source :
- Journal of Geometry and Physics [ 0393-0440 ] ; 1997.
Abstract
This article, in conjunction with a previous one, proves Drinfeld's theorems about invariant star products, ISPS, on a connected Lie group G endowed with an invariant symplectic structure β1 ϵZ2(g). In particular, we prove that every formal 2-cocycle β h ̵ ϵ β1 + h ̵ · Z2 (g))[[ħ]] determines an ISP, Fβ h ̵, and conversely any ISP, F, determines a formal 2-cocycle fx360-1 such that F is equivalent to Fω h ̵. We also prove that two ISPS Fβ h ̵ and Fω h ̵ are equivalent if and only if the cohomology classes of β h ̵ and ω h ̵ coincide. These properties define a bijection between the set of equivalent classes of ISP on (G; β1) and the set β1 + h ̵ · H2(g)[[ħ]].
Url:
DOI: 10.1016/S0393-0440(97)80010-1
Affiliations:
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