Quantum function algebras as quantum enveloping algebras

Details Quantum function algebras as quantum enveloping algebras Quantum function algebras as quantum enveloping algebras

1997-01-10

arxiv.org/abs/q-alg/9701010v2

Mathematics

Quantum Algebra

26 pages, AMS-TeX C, Version 3.0 (to appear in "Communications in Algebra"). Some important formulas in sections 1 and 4 have

Scientific paper

Inspired by a result in the same author's previous work q-alg/9604009, we locate two $ k[q,q^{-1}] $--integer forms of $ F_q[SL(n+1)] $, along with a presentation by generators and relations, and prove that for $ q=1 $ they specialize to $ U({\frak h}) $, where $ {\frak h} $ is the Lie bialgebra of the Poisson Lie group $ H $ dual of $ SL(n+1) $; moreover, we explain the relation with [loc.cit.]. In sight of this, we prove two PBW-like theorems for $ F_q[SL(n+1)] $, both related to the classical PBW theorem for $ U({\frak h}) $.

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