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Quantum-classical interations and Galois type extensions. (English) Zbl 1069.81540
Hajac, Piotr M. (ed.) et al., Noncommutative geometry and quantum groups. Proceedings of the Banach Center school/conference, Warsaw, Poland, September 17–29, 2001. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 61, 103-109 (2003).
Summary: An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle interactions.
For the entire collection see [Zbl 1024.00070].
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
12F10 Separable extensions, Galois theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations