bicovariant differential calculus
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2020 ◽  
Vol 563 ◽  
pp. 198-250
Author(s):  
Jyotishman Bhowmick ◽  
Sugato Mukhopadhyay


2017 ◽  
Vol 58 (7) ◽  
pp. 071701 ◽  
Author(s):  
Stjepan Meljanac ◽  
Saša Krešić–Jurić ◽  
Tea Martinić


2016 ◽  
Vol 15 (09) ◽  
pp. 1650172 ◽  
Author(s):  
Salih Celik

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.



2016 ◽  
Vol 13 (03) ◽  
pp. 1650029
Author(s):  
Ergün Yasar

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.



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


2011 ◽  
Vol 23 (06) ◽  
pp. 575-613 ◽  
Author(s):  
GIOVANNI LANDI ◽  
ALESSANDRO ZAMPINI

We describe Laplacian operators on the quantum group SUq(2) equipped with the four-dimensional bicovariant differential calculus of Woronowicz as well as on the quantum homogeneous space [Formula: see text] with the restricted left covariant three-dimensional differential calculus. This is done by giving a family of Hodge dualities on both the exterior algebras of SUq(2) and [Formula: see text]. We also study gauged Laplacian operators acting on sections of line bundles over the quantum sphere.



2007 ◽  
Vol 04 (07) ◽  
pp. 1087-1097 ◽  
Author(s):  
Z. BENTALHA ◽  
M. TAHIRI

When reviewing the work of Aschieri–Castellani concerning the bicovariant differential calculus on GLq(2), we remarked that a peculiar basis within the space of quantum one-forms over SUq(2) can lead to a new bicovariant differential calculus on SUq(2) easy to handle than those known in the literature. New results have been obtained for the exterior product, the exterior differential, the C-structure constants, the Cartan–Maurer equations, and the q-Lie algebra.



1996 ◽  
Vol 11 (06) ◽  
pp. 1019-1056 ◽  
Author(s):  
PAOLO ASCHIERI ◽  
LEONARDO CASTELLANI

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).



1996 ◽  
Vol 46 (2-3) ◽  
pp. 201-208 ◽  
Author(s):  
Piotr Kosiński ◽  
Paweł Maślanka ◽  
Jan Sobczyk


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