The set of equivalent classes of invariant star products on (G; β1)

✍ Scribed by Carlos Moreno; Luis Valero

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 956 KB
• Volume: 23
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(97)80010-1

✦ Synopsis

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 PI E Z*(n). In particular, we prove that every formal 2-cocycle & E PI + A Z*(g)) [[h]] determines an ISP, FBfi, and conversely any ISP, F, determines a formal 2-cocycle m E p1 + A Z"(g) [[h]] such that F is equivalent to F% . We also prove that two ISPS FBh and FQ are equivalent if and only if the cohomology classes of /& and m coincide. These properties define a bijection between the set of equivalent classes of ISP on (G; PI) and the set ,& + h 'Ft2(g) [[h]].