The realizations of quantum groups of An−1 and Cn types in q‐deformed oscillator systems at classical and quantum levels

1991 ◽  
Vol 32 (12) ◽  
pp. 3241-3245 ◽  
Author(s):  
Zhe Chang ◽  
Jian‐Xiong Wang ◽  
Hong Yan
Keyword(s):  
Quantum Groups ◽  
Deformed Oscillator

INTERPOLATING STATISTICS AND q-DEFORMED OSCILLATOR ALGEBRAS

2006 ◽  
Vol 20 (06) ◽  
pp. 697-713 ◽  
Author(s):  
P. NARAYANA SWAMY
Keyword(s):  
Quantum Groups ◽  
Thermodynamic Functions ◽  
Oscillator Algebra ◽  
Fermi Statistics ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra ◽  
Continuous Interpolation ◽  
Outstanding Issue ◽  
Derivatives Of ◽  
Oscillator Algebras

The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra, or quantum groups, has been an outstanding issue. We are able to demonstrate that a q-deformed oscillator algebra can be used to describe the statistics of particles which provide a continuous interpolation between Bose and Fermi statistics. We show that the generalized intermediate statistics splits into Boson-like and Fermion-like regimes, each described by a unique oscillator algebra. The thermostatistics of Boson-like particles is described by employing q-calculus based on the Jackson derivative while the Fermion-like particles are described by ordinary derivatives of thermodynamics. Thermodynamic functions for systems of both types are determined and examined.

scholarly journals Curved Rickard complexes and link homologies

2020 ◽  
Vol 2020 (769) ◽  
pp. 87-119
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Joshua Sussan
Keyword(s):  
Spectral Sequence ◽  
Quantum Groups ◽  
Braid Group ◽  
Derived Categories ◽  
Duke Math ◽  
Khovanov Homology ◽  
Hilbert Schemes ◽  
Coherent Sheaves ◽  
Knot Homology ◽  
Original Motivation

AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).

scholarly journals Symmetries and integrals of motion of a superintegrable deformed oscillator

2021 ◽  
pp. 168428
Author(s):  
Joanna Gonera ◽  
Artur Jasiński ◽  
Piotr Kosiński
Keyword(s):  
Integrals Of Motion ◽  
Deformed Oscillator

scholarly journals Bialgebra cohomology, deformations, and quantum groups.

1990 ◽  
Vol 87 (1) ◽  
pp. 478-481 ◽  
Author(s):  
M. Gerstenhaber ◽  
S. D. Schack
Keyword(s):  
Quantum Groups
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