Results 21 to 30 of about 96,588 (331)
On the algebraic structure of differential calculus on quantum groups [PDF]
Journal of Mathematical Physics, 1997 Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups—coordinate functions, differential 1-forms, Lie derivatives, and inner derivations—as the cross-product algebra of two mutually dual graded Hopf ...
Olga Radko, Alexey Vladimirov
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Quantum Affine Transformation Group and Covariant Differential Calculus [PDF]
Progress of Theoretical Physics, 1994 LaTeX 22 pages OS-GE-34-94 RCNP ...
N. Aizawa, Haru-Tada Sato
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Differential calculus on the quantum superspace and deformation of phase space [PDF]
Zeitschrift f�r Physik C Particles and Fields, 1992 We investigate non-commutative differential calculus on the supersymmetric version of quantum space where the non-commuting super-coordinates consist of bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum deformation of the general linear supergroup, $GL_q(m|n)$, is studied and the explicit form for the ${\hat R}$-matrix ...
Tatsuo Kobayashi, Tsuneo Uematsu
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Fock space representation of differential calculus on the noncommutative quantum space [PDF]
Journal of Mathematical Physics, 1997 A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed.
Amrit Kumar Mishra, G. Rajasekaran
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DIFFERENTIAL CALCULUS AND CONNECTIONS ON A QUANTUM PLANE AT A CUBIC ROOT OF UNITY [PDF]
Reviews in Mathematical Physics, 2000 We consider the algebra of N×N matrices as a reduced quantum plane on which a finite-dimensional quantum group ℋ acts. This quantum group is a quotient of [Formula: see text], q being an Nth root of unity. Most of the time we shall take N=3; in that case dim(ℋ)=27.
Robert Coquereaux +2 more
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, 2020 In this study, we investigate the sum-type singular nonlinear fractional q-integro-differential $m$-point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo $q$-derivative ...
Ali Ahmadian +3 more
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COMMENT ON THE DIFFERENTIAL CALCULUS ON THE QUANTUM EXTERIOR PLANE [PDF]
Modern Physics Letters A, 1998 We give a two-parameter quantum deformation of the exterior plane and its differential calculus without the use of any R-matrix and relate it to the differential calculus with the R-matrix. We prove that there are two types of solutions of the Yang–Baxter equation whose symmetry group is GL p,q(2).
Salih Çelïk +2 more
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Hidden symmetry of the differential calculus on the quantum matrix space [PDF]
Journal of Physics A: Mathematical and General, 1997 A standard bicovariant differential calculus on a quantum matrix space ${\tt Mat}(m,n)_q$ is considered. The principal result of this work is in observing that the $U_q\frak{s}(\frak{gl}_m\times \frak{gl}_n))_q$ is in fact a $U_q\frak{sl}(m+n)$-module differential algebra.
S. Sinel’shchikov, L. Vaksman
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BRST operator for quantum Lie algebras and differential calculus on quantum groups
Theoretical and Mathematical Physics, 2001 20 pages, LaTeX, Lecture given at the Workshop on "Classical and Quantum Integrable Systems", 8 - 11 January, Protvino, Russia; corrected some ...
A. P. Isaev, O. Ogievetsky
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Differential calculus on compact matrix pseudogroups (quantum groups) [PDF]
Communications in Mathematical Physics, 1989 This is a sequel to an earlier paper by the author [ibid. 111, No. 4, 613-665 (1987; Zbl 0627.58034)]. There, he introduced and developed the finite-dimensional representation theory of a particular generalization of the concept of a compact Lie group, which has the desirable property of admitting nontrivial deformations.
S. Woronowicz
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