The Role of Solvable Groups in Quantization of Lie Algebras

Details The Role of Solvable Groups in Quantization of Lie Algebras The Role of Solvable Groups in Quantization of Lie Algebras

1994-05-06

arxiv.org/abs/hep-th/9405044v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages. To be published in "Zapiski Nauchn. Semin. POMI", V.209

Scientific paper

The elements of the wide class of quantum universal enveloping algebras are prooved to be Hopf algebras $H$ with spectrum $Q(H)$ in the category of groups. Such quantum algebras are quantum groups for simply connected solvable Lie groups $P(H)$. This provides utilities for a new algorithm of constructing quantum algebras especially useful for nonsemisimple ones. The quantization procedure can be carried out over an arbitrary field. The properties of the algorithm are demonstrated on examples.

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