Obstructions for Twist Star Products

Abstract

In this short note we point out that not every star product is induced by a Drinfel'd twist by showing that not every Poisson structure is induced by a classical $r$-matrix. Examples include the higher genus symplectic Pretzel surfaces and the symplectic sphere ${\mathbb{S}}^2$.

8 pages, comments are welcome

Cited by in corpus (5)

• Braided Cartan Calculi and Submanifold Algebras
• Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
• Twisted submanifolds of R^n
• Twisted Quadrics and Algebraic Submanifolds in ${\mathbb{R}}^n$
• Characteristic (Fedosov-)class of a twist constructed by Drinfel'd