Some quantum analogues of solvable Lie groups

Details Some quantum analogues of solvable Lie groups Some quantum analogues of solvable Lie groups

1993-08-27

arxiv.org/abs/hep-th/9308138v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras of twisted polynomials with a derivation, an object which has often appeared in the general theory of non-commutative rings. In particular, we find maximal dimensions of their irreducible representations. Our results confirm the validity of the general philosophy that the representation theory is intimately connected to the Poisson geometry.

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