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Mathematische Gesellschaft
Drinfel'd Twist: Strength and Limits
6.7.2017, 16:15 - 17:15
Speaker:Dr. Chiara Esposito, Universit├Ąt W├╝rzburg
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Organizer:Mathematisches Institut
Abstract: Deformation quantization has been introduced in the seventies with the aim of quantizing classical mechanical systems. The main idea consists in constructing a new non-commutative product, called star product, which deforms the standard pointwise one and encodes the information of classical dynamics. A special class of star products is the one induced by symmetries, as introduced by Drinfel'd.
Drinfel'd approach consists in defining a new tool called twist which deforms the Hopf algebra structure of the universal enveloping algebra and, as a consequence, of any module algebra.
I will explain the strength of this method, as it defines a star product in a very simple and elegant way, and its algebraic and geometrical features. Nevertheless, I will point out that not every star product can be induced by a Drinfel'd twist and provide concrete counterexamples. In spite of the fact that twist is defined in a purely algebraic setting, it is interesting to observe that the obstructions lie in the realm of symplectic geometry.
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