2008
DOI: 10.1088/1751-8113/41/30/304038
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From quantum universal enveloping algebras to quantum algebras

Abstract: The "local" structure of a quantum group G q is currently considered to be an infinite-dimensional object: the corresponding quantum universal enveloping algebra U q (g), which is a Hopf algebra deformation of the universal enveloping algebra of a n-dimensional Lie algebra g = Lie(G). However, we show how, by starting from the generators of the underlying Lie bialgebra (g, δ), the analyticity in the deformation parameter(s) allows us to determine in a unique way a set of n "almost primitive" basic objects in U… Show more

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Cited by 5 publications
(11 citation statements)
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“…This fact did not allow in the past the construction of q-Poisson analogues for algebras of rank greater than one. However, the analytical bases approach presented in [24,25] provides a quantization framework based on pure commutators, thus leading to a well-…”
Section: Discussionmentioning
confidence: 99%
See 2 more Smart Citations
“…This fact did not allow in the past the construction of q-Poisson analogues for algebras of rank greater than one. However, the analytical bases approach presented in [24,25] provides a quantization framework based on pure commutators, thus leading to a well-…”
Section: Discussionmentioning
confidence: 99%
“…Given an arbitrary Lie bialgebra (g, δ) the quantum algebra (U z (g), ∆ z ) (that is obtained through the analytic procedure described in [24,25]) is the Hopf algebra deformation (U z (g), ∆ z ) of the universal enveloping algebra of g, U(g), compatible with the deformed coproduct ∆ z (X) whose leading order terms are…”
Section: Quantum Algebras and Poisson-hopf Limitmentioning
confidence: 99%
See 1 more Smart Citation
“…To enlighten the construction we discuss explicitly the quantization of the Lie bialgebra (su(2), δ) described by (2.8) with α = 1 and (2.9). More details can be found in [5]. The results of this Section show that analyticity chooses the coproduct given by formula (3.2) among all possible ones [1] and the usual expressions (3.1) must be replaced by other slightly different ones.…”
Section: Analytical Deformationmentioning
confidence: 94%
“…In this "physically" motivated work we summarize a research line devoted to individuate, for both Lie and quantum algebras, these basic objects -the generators-in an intrinsic way eliminating every arbitrariness. In this review we do not describe all the technical details of this approach and the interested reader is invited to look at the specific papers quoted in the bibliography [1]- [5].…”
Section: Introductionmentioning
confidence: 99%