scholarly journals Two-parameter families of quantum symmetry groups

2011 ◽  
Vol 260 (11) ◽  
pp. 3252-3282 ◽  
Author(s):  
Teodor Banica ◽  
Adam Skalski
Keyword(s):  
Symmetry Groups ◽  
Quantum Symmetry ◽  
Two Parameter

Classical and quantum symmetry groups of a free‐fall particle

1985 ◽  
Vol 26 (1) ◽  
pp. 55-61
Author(s):  
Toshihiro Iwai ◽  
See‐Gew Rew
Keyword(s):  
Free Fall ◽  
Symmetry Groups ◽  
Quantum Symmetry

scholarly journals Quantum symmetries on noncommutative complex spheres with partial commutation relations

2018 ◽  
Vol 21 (04) ◽  
pp. 1850028
Author(s):  
Simeng Wang
Keyword(s):  
Quantum Groups ◽  
Unitary Groups ◽  
Symmetry Groups ◽  
Orthogonal Groups ◽  
Commutation Relations ◽  
Quantum Symmetry ◽  
Quantum Symmetries ◽  
Free Independence

We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial commutation relations. We also discuss some geometric aspects of the quantum orthogonal groups associated with the mixture of classical and free independence discovered by Speicher and Weber. We show that these quantum groups are quantum symmetry groups on some quantum spaces of spherical vectors with partial commutation relations.

scholarly journals Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras

2014 ◽  
Vol 17 (02) ◽  
pp. 1450012 ◽  
Author(s):  
Adam Skalski ◽  
Piotr M. Sołtan
Keyword(s):  
Hopf Algebras ◽  
Discrete Group ◽  
Inductive Limit ◽  
Symmetric Groups ◽  
Projective Limit ◽  
Symmetry Groups ◽  
C Algebras ◽  
Quantum Symmetry ◽  
Doubling Construction ◽  
Projective Limits

The quantum symmetry group of the inductive limit of C*-algebras equipped with orthogonal filtrations is shown to be the projective limit of the quantum symmetry groups of the C*-algebras appearing in the sequence. Some explicit examples of such projective limits are studied, including the case of quantum symmetry groups of the duals of finite symmetric groups, which do not fit directly into the framework of the main theorem and require further specific study. The investigations reveal a deep connection between quantum symmetry groups of discrete group duals and the doubling construction for Hopf algebras.

Some results of the Barbier-Chalonge-Divan system of stellar classification

1966 ◽  
Vol 24 ◽  
pp. 77-90 ◽  
Author(s):  
D. Chalonge
Keyword(s):  
Early Type ◽  
Parameter System ◽  
Early Type Stars ◽  
Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

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