scholarly journals Quasitriangularity and enveloping algebras for inhomogeneous quantum groups

1996 ◽  
Vol 37 (9) ◽  
pp. 4724-4737
Author(s):  
P. Podleś
Keyword(s):  
Quantum Groups ◽  
Enveloping Algebras ◽  
Inhomogeneous Quantum

scholarly journals On the Structure of Inhomogeneous Quantum Groups

1997 ◽  
Vol 185 (2) ◽  
pp. 325-358 ◽  
Author(s):  
P. Podleś ◽  
S. L. Woronowicz
Keyword(s):  
Quantum Groups ◽  
Inhomogeneous Quantum

Inhomogeneous quantum groups

1992 ◽  
Vol 42 (12) ◽  
pp. 1303-1312 ◽  
Author(s):  
Bernhard Drabant ◽  
Michael Schlieker ◽  
Wolfgang Weich ◽  
Ralf Weixler
Keyword(s):  
Quantum Groups ◽  
Inhomogeneous Quantum

INHOMOGENEOUS QUANTUM GROUP GENERALIZATION OF IO(2n,ℂ) AND ISp(2n,ℂ)

2008 ◽  
Vol 23 (08) ◽  
pp. 617-622 ◽  
Author(s):  
AZMI ALI ALTINTAṢ ◽  
METIN ARIK
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Inhomogeneous Quantum

We consider an extension of orthogonal and symplectic inhomogeneous groups into quantum groups with noncommuting inhomogeneous parameters. The quantum subgroups of these quantum groups are investigated.

scholarly journals Inhomogeneous quantum groups as symmetries of phonons

1992 ◽  
Vol 68 (25) ◽  
pp. 3718-3720 ◽  
Author(s):  
F. Bonechi ◽  
E. Celeghini ◽  
R. Giachetti ◽  
E. Sorace ◽  
M. Tarlini
Keyword(s):  
Quantum Groups ◽  
Inhomogeneous Quantum

scholarly journals Twisted deformations vs. cocycle deformations for quantum groups

2020 ◽  
pp. 2050084
Author(s):  
Gastón Andrés García ◽  
Fabio Gavarini
Keyword(s):  
Hopf Algebra ◽  
Quantum Groups ◽  
Algebra Structure ◽  
Universal Enveloping Algebras ◽  
Theoretical Terms ◽  
Enveloping Algebras ◽  
Coalgebra Structure ◽  
Quantized Universal Enveloping Algebras

In this paper, we study two deformation procedures for quantum groups: deformations by twists, that we call “comultiplication twisting”, as they modify the coalgebra structure, while keeping the algebra one — and deformations by [Formula: see text]-cocycle, that we call “multiplication twisting”, as they deform the algebra structure, but save the coalgebra one. We deal with quantized universal enveloping algebras (in short QUEAs), for which we accordingly consider those arising from twisted deformations (in short TwQUEAs) and those arising from [Formula: see text]-cocycle deformations, usually called multiparameter QUEAs (in short MpQUEAs). Up to technicalities, we show that the two deformation methods are equivalent, in that they eventually provide isomorphic outputs, which are deformations (of either kinds) of the “canonical”, well-known one-parameter QUEA by Jimbo and Lusztig. It follows that the two notions of TwQUEAs and of MpQUEAs — which, in Hopf algebra theoretical terms are naturally dual to each other — actually coincide; thus, that there exists in fact only one type of “pluriparametric deformation” for QUEAs. In particular, the link between the realization of any such QUEA as a MpQUEA and that as a TwQUEA is just a (very simple, and rather explicit) change of presentation.

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