scholarly journals Derivations of the Positive Part of the Two-parameter Quantum Group of Type G2

2021 ◽  
Vol 37 (9) ◽  
pp. 1471-1484
Author(s):  
Yong Yue Zhong ◽  
Xiao Min Tang
Keyword(s):  
Quantum Group ◽  
Positive Part ◽  
Two Parameter

scholarly journals A TWO-PARAMETER DEFORMED SUSY ALGEBRA FOR SUp/q(n)-COVARIANT (p,q)-DEFORMED FERMIONIC OSCILLATORS

2005 ◽  
Vol 20 (08) ◽  
pp. 613-622 ◽  
Author(s):  
ABDULLAH ALGIN ◽  
METIN ARIK
Keyword(s):  
Quantum Group ◽  
Fock Space ◽  
Space Representation ◽  
Oscillator Algebra ◽  
Two Parameter

We construct a two-parameter deformed SUSY algebra by constructing SUSY generators which are bilinears of n (p,q)-deformed fermions covariant under the quantum group SU p/q(n) and n undeformed bosons. The Fock space representation of the algebra constructed is discussed and the total deformed Hamiltonian for such a system is obtained. Some physical applications of the quantum group covariant two-parameter deformed fermionic oscillator algebra are also considered.

On the combinatorial rank of the quantum groups of type G2

2020 ◽  
pp. 2150208
Author(s):  
Vanusa Dylewski ◽  
Barbara Pogorelsky ◽  
Carolina Renz
Keyword(s):  
Quantum Group ◽  
Lie Algebra ◽  
Quantum Groups ◽  
Main Parameter ◽  
Positive Part ◽  
Simple Lie Algebra ◽  
Type Formula ◽  
Part Formula ◽  
Multiplicative Order

In this paper, we calculate the combinatorial rank of the positive part [Formula: see text] of the multiparameter version of the small Lusztig quantum group, where [Formula: see text] is a simple Lie algebra of type [Formula: see text]. Supposing that the main parameter of quantization [Formula: see text] has multiplicative order [Formula: see text], where [Formula: see text] is finite, [Formula: see text], we prove that the combinatorial rank equals 3.

Thermodynamics of two parameter quantum group gases

2002 ◽  
Vol 300 (4-5) ◽  
pp. 392-396 ◽  
Author(s):  
M. Arik ◽  
J. Kornfilt
Keyword(s):  
Quantum Group ◽  
Two Parameter

scholarly journals On the centre of two-parameter quantum groups

2006 ◽  
Vol 136 (3) ◽  
pp. 445-472 ◽  
Author(s):  
Georgia Benkart ◽  
Seok-Jin Kang ◽  
Kyu-Hwan Lee
Keyword(s):  
Quantum Groups ◽  
Polynomial Ring ◽  
Bilinear Form ◽  
Skew Polynomial Ring ◽  
Positive Part ◽  
Invariant Bilinear Form ◽  
Central Elements ◽  
Skew Polynomial ◽  
Two Parameter

We describe Poincaré–Birkhoff–Witt bases for the two-parameter quantum groups U = Ur,s(sln) following Kharchenko and show that the positive part of U has the structure of an iterated skew polynomial ring. We define an ad-invariant bilinear form on U, which plays an important role in the construction of central elements. We introduce an analogue of the Harish-Chandra homomorphism and use it to determine the centre of U.

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