scholarly journals Bicovariant quantum algebras and quantum Lie algebras

1993 ◽  
Vol 157 (2) ◽  
pp. 305-329 ◽  
Author(s):  
Peter Schupp ◽  
Paul Watts ◽  
Bruno Zumino
Keyword(s):  
Lie Algebras ◽  
Quantum Algebras ◽  
Quantum Lie Algebras

Quantum algebra embeddings: deforming functionals and algebraic approach

1994 ◽  
Vol 72 (7-8) ◽  
pp. 519-526 ◽  
Author(s):  
J. Van der Jeugt
Keyword(s):  
Hypergeometric Function ◽  
Lie Algebras ◽  
Algebraic Approach ◽  
Quantum Algebra ◽  
Physical Models ◽  
Quantum Algebras ◽  
Basic Hypergeometric Function

The study of subalgebras of Lie algebras arising in physical models has been important for many applications. In the present paper we examine the q-deformation of such embeddings; the Lie algebras are then replaced by quantum algebras. Two methods are presented: one based upon deforming functionals, and a direct algebraic approach. A number of examples are given, e.g., [Formula: see text] and [Formula: see text]. For the last example, we give the q-boson construction, and the relevant overlap coefficients are related to a generalized basic hypergeometric function [Formula: see text].

scholarly journals On quantum Lie algebras and quantum root systems

1996 ◽  
Vol 29 (8) ◽  
pp. 1703-1722 ◽  
Author(s):  
Gustav W Delius ◽  
Andreas Hüffmann
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Quantum Lie Algebras

scholarly journals Quantum counterparts of three-dimensional real Lie algebras over harmonic oscillator

Open Physics ◽  
2010 ◽  
Vol 8 (3) ◽  
Author(s):  
Eugen Paal ◽  
Jüri Virkepu
Keyword(s):  
Harmonic Oscillator ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Quantum Algebras ◽  
Jacobi Operators

AbstractOperadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional (3D) real Lie algebras in Bianchi classification. The Jacobi operators of the quantum algebras are found.

scholarly journals -Deformed quantum Lie algebras

2006 ◽  
Vol 56 (11) ◽  
pp. 2289-2325 ◽  
Author(s):  
Alexander Schmidt ◽  
Hartmut Wachter
Keyword(s):  
Lie Algebras ◽  
Quantum Lie Algebras

scholarly journals The structure of quantum Lie algebras for the classical series , and

1998 ◽  
Vol 31 (8) ◽  
pp. 1995-2019 ◽  
Author(s):  
Gustav W Delius ◽  
Christopher Gardner ◽  
Mark D Gould
Keyword(s):  
Lie Algebras ◽  
Quantum Lie Algebras

Some quantum Lie algebras of typeDnpositive

2003 ◽  
Vol 36 (9) ◽  
pp. 2271-2287
Author(s):  
C sar Bautista ◽  
Mar a Araceli Juar z-Ram rez
Keyword(s):  
Lie Algebras ◽  
Quantum Lie Algebras

BRST OPERATOR FOR QUANTUM LIE ALGEBRAS: EXPLICIT FORMULA

2004 ◽  
Vol 19 (supp02) ◽  
pp. 240-247 ◽  
Author(s):  
A. P. ISAEV ◽  
O. OGIEVETSKY
Keyword(s):  
Quantum Group ◽  
Recurrence Relation ◽  
Explicit Formula ◽  
Lie Algebras ◽  
Important Class ◽  
Quadratic Algebras ◽  
Brst Operator ◽  
Quantum Lie Algebras

We continue our study of quantum Lie algebras, an important class of quadratic algebras arising in the Woronowicz calculus on a quantum group. Quantum Lie algebras are generalizations of Lie (super)algebras. Many notions from the theory of Lie (super)algebras admit "quantum" analogues. In particular, there is a BRST operator Q(Q2=0) which generates the differential in the Woronowicz theory and gives information about (co)homologies of quantum Lie algebras. In our previous papers a recurrence relation for the operator Q for quantum Lie algebras was given. Here we solve this recurrence relation and obtain an explicit formula for the BRST operator.

scholarly journals New realizations of algebras of the Askey–Wilson type in terms of Lie and quantum algebras

2020 ◽  
pp. 2150002
Author(s):  
Nicolas Crampé ◽  
Dounia Shaaban Kabakibo ◽  
Luc Vinet
Keyword(s):  
Orthogonal Polynomials ◽  
Lie Algebras ◽  
Recurrence Relations ◽  
Rational Functions ◽  
The Other ◽  
Quantum Algebras ◽  
Casimir Element ◽  
Usual Representation ◽  
Racah Algebra

The Askey–Wilson algebra is realized in terms of the elements of the quantum algebras [Formula: see text] or [Formula: see text]. A new realization of the Racah algebra in terms of the Lie algebras [Formula: see text] or [Formula: see text] is also given. Details for different specializations are provided. The advantage of these new realizations is that one generator of the Askey–Wilson (or Racah) algebra becomes diagonal in the usual representation of the quantum algebras whereas the second one is tridiagonal. This allows us to recover easily the recurrence relations of the associated orthogonal polynomials of the Askey scheme. These realizations involve rational functions of the Cartan generator of the quantum algebras, where they are linear with respect to the other generators and depend on the Casimir element of the quantum algebras.

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