scholarly journals Exponentiations over the quantum algebra U q (sl 2 (ℂ))

10.5802/cml.8 ◽  
2017 ◽  
Vol 5 (2) ◽  
pp. 49-77
Author(s):  
Sonia L’Innocente ◽  
Françoise Point ◽  
Carlo Toffalori
Keyword(s):  
Quantum Algebra

A quantum algebra approach to basic multivariable special functions

1994 ◽  
Vol 27 (20) ◽  
pp. 6781-6797 ◽  
Author(s):  
R Floreanini ◽  
L Lapointe ◽  
L Vinet
Keyword(s):  
Special Functions ◽  
Quantum Algebra ◽  
Algebra Approach

LORENTZ COVARIANCE FOR THE QUANTUM ALGEBRA OF OBSERVABLES: NAMBU–GOTO STRINGS IN 3 + 1 DIMENSIONS

2002 ◽  
Vol 17 (17) ◽  
pp. 2331-2349 ◽  
Author(s):  
GERRIT HANDRICH
Keyword(s):  
Rest Frame ◽  
Poisson Algebra ◽  
Quantum Algebra ◽  
Substantial Part ◽  
Quantum Case ◽  
Generators And Relations ◽  
Defining Relations ◽  
Algebra Of Observables ◽  
The One ◽  
The Relationship

To postulate correspondence for the observables only is a promising approach to a fully satisfying quantization of the Nambu–Goto string. The relationship between the Poisson algebra of observables and the corresponding quantum algebra is established in the language of generators and relations. A very valuable tool is the transformation to the string's rest frame, since a substantial part of the relations are solved. It is the aim of this paper to clarify the relationship between the fully covariant and the rest frame description. Both in the classical and in the quantum case, an efficient method for recovering the covariant algebra from the one in the rest frame is described. Restrictions on the quantum defining relations are obtained, which are not taken into account when one postulates correspondence for the rest frame algebra. For the part of the algebra studied up to now in explicit computations, these further restrictions alone determine the quantum algebra uniquely — in full consistency with the further restrictions found in the rest frame.

scholarly journals THE ADJOINT REPRESENTATION OF QUANTUM ALGEBRA Uq(sl(2))

2009 ◽  
Vol 16 (1) ◽  
pp. 63-75 ◽  
Author(s):  
Č. BURDÍK ◽  
O. NAVRÁTIL ◽  
S. POŠTA
Keyword(s):  
Adjoint Representation ◽  
Quantum Algebra
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