scholarly journals The Quantum Cartan Algebra Associated to a Bicovariant Differential Calculus

2011 ◽  
Vol 68 (3) ◽  
pp. 319-346
Author(s):  
Lucio S. Cirio ◽  
Chiara Pagani ◽  
Alessandro Zampini
Keyword(s):  
Differential Calculus ◽  
Bicovariant Differential Calculus

Bicovariant differential calculus on the quantum superspace ℝq(1|2)

2016 ◽  
Vol 15 (09) ◽  
pp. 1650172 ◽  
Author(s):  
Salih Celik
Keyword(s):  
Hopf Algebra ◽  
Differential Calculus ◽  
Vector Fields ◽  
Lie Superalgebra ◽  
Function Algebra ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Bicovariant Differential Calculus ◽  
Quantum Supergroup ◽  
Dual Hopf Algebra

Super-Hopf algebra structure on the function algebra on the extended quantum superspace has been defined. It is given a bicovariant differential calculus on the superspace. The corresponding (quantum) Lie superalgebra of vector fields and its Hopf algebra structure are obtained. The dual Hopf algebra is explicitly constructed. A new quantum supergroup that is the symmetry group of the differential calculus is found.

Bicovariant differential calculus on quantum groupsSU q (N) andSO q (N)

1991 ◽  
Vol 142 (3) ◽  
pp. 605-641 ◽  
Author(s):  
Ursula Carow-Watamura ◽  
Michael Schlieker ◽  
Satoshi Watamura ◽  
Wolfgang Weich
Keyword(s):  
Differential Calculus ◽  
Bicovariant Differential Calculus

Bicovariant differential calculus on quantum groups and wave mechanics

1992 ◽  
Vol 42 (12) ◽  
pp. 1279-1288
Author(s):  
Ursula Carow-Watamura ◽  
Satoshi Watamura ◽  
Arthur Hebecker ◽  
Michael Schlieker ◽  
Wolfgang Weich
Keyword(s):  
Quantum Groups ◽  
Differential Calculus ◽  
Wave Mechanics ◽  
Bicovariant Differential Calculus

A Two-parameter bicovariant differential calculus on the (1 + 2)-dimensional q-superspace

2016 ◽  
Vol 13 (03) ◽  
pp. 1650029
Author(s):  
Ergün Yasar
Keyword(s):  
Hopf Algebra ◽  
Differential Calculus ◽  
Lie Superalgebra ◽  
Point Of View ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Bicovariant Differential Calculus ◽  
Two Parameter

We construct a two-parameter bicovariant differential calculus on [Formula: see text] with the help of the covariance point of view using the Hopf algebra structure of [Formula: see text]. To achieve this, we first use the consistency of calculus and the approach of [Formula: see text]-matrix which satisfies both ungraded and graded Yang–Baxter equations. In particular, based on this differential calculus, we investigate Cartan–Maurer forms for this [Formula: see text]-superspace. Finally, we obtain the quantum Lie superalgebra corresponding the Cartan–Maurer forms.

scholarly journals INHOMOGENEOUS QUANTUM GROUPS IGLq,r(N): UNIVERSAL ENVELOPING ALGEBRA AND DIFFERENTIAL CALCULUS

1996 ◽  
Vol 11 (06) ◽  
pp. 1019-1056 ◽  
Author(s):  
PAOLO ASCHIERI ◽  
LEONARDO CASTELLANI
Keyword(s):  
Quantum Group ◽  
Differential Calculus ◽  
Matrix Elements ◽  
Dual Algebra ◽  
Enveloping Algebra ◽  
Bicovariant Differential Calculus ◽  
Group Matrix ◽  
Single Structure ◽  
Real Forms ◽  
Inhomogeneous Quantum

A review of the multiparametric linear quantum group GL q,r(N), its real forms, its dual algebra U [ gl q,r(N)] and its bicovariant differential calculus is given in the first part of the paper. We then construct the (multiparametric) linear inhomogeneous quantum group IGL q,r(N) as a projection from GL q,r(N+1) or, equivalently, as a quotient of GL q,r(N+1) with respect to a suitable Hopf algebra ideal. A bicovariant differential calculus on IGL q,r(N) is explicitly obtained as a projection from that on GL q,r(N+1). Our procedure unifies in a single structure the quantum plane coordinates and the q group matrix elements [Formula: see text], and allows one to deduce without effort the differential calculus on the q plane IGL q,r(N)/ GL q,r(N). The general theory is illustrated on the example of IGL q,r(2).

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