The role of solvable groups in quantization of Lie algebras
Copyright policy )The role of solvable groups in quantization of Lie algebras
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.
10 pages. To be published in "Zapiski Nauchn. Semin. POMI", V.209
- St Petersburg University Russian Federation
High Energy Physics - Theory, Mathematics - Algebraic Geometry, quantum groups, High Energy Physics - Theory (hep-th), Hopf algebras, FOS: Mathematics, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, simply connected solvable Lie groups, Algebraic Geometry (math.AG), Hopf algebras (associative rings and algebras)
High Energy Physics - Theory, Mathematics - Algebraic Geometry, quantum groups, High Energy Physics - Theory (hep-th), Hopf algebras, FOS: Mathematics, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, simply connected solvable Lie groups, Algebraic Geometry (math.AG), Hopf algebras (associative rings and algebras)
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