scholarly journals “Classical” Flag Varieties for Quantum Groups: The Standard Quantum SL(n,C)

2002 ◽  
Vol 171 (1) ◽  
pp. 103-138 ◽  
Author(s):  
Christian Ohn
Keyword(s):  
Quantum Groups ◽  
Flag Varieties ◽  
Standard Quantum

scholarly journals Twisting 2-cocycles for the construction of new non-standard quantum groups

1997 ◽  
Vol 38 (10) ◽  
pp. 5383-5401 ◽  
Author(s):  
Andrew D. Jacobs ◽  
J. F. Cornwell
Keyword(s):  
Quantum Groups ◽  
Standard Quantum

scholarly journals A CLOSED EXPRESSION FOR THE UNIVERSAL ℛ-MATRIX IN A NON-STANDARD QUANTUM DOUBLE

1993 ◽  
Vol 08 (27) ◽  
pp. 2573-2578 ◽  
Author(s):  
A.A. VLADIMIROV
Keyword(s):  
Quantum Group ◽  
Lie Algebra ◽  
Quantum Groups ◽  
Hopf Algebras ◽  
Reduced Form ◽  
Elementary Functions ◽  
Quantum Double ◽  
Closed Expression ◽  
Standard Quantum ◽  
Number Of Generators

In recent papers by the author, a method was developed for constructing quasitriangular Hopf algebras (quantum groups) of the quantum-double type. As a by-product, a novel non-standard example of the quantum double has been found. In this letter, a closed expression (in terms of elementary functions) for the corresponding universal ℛ-matrix is obtained. In reduced form, when the number of generators becomes two instead of four, this quantum group can be interpreted as a deformation of the Lie algebra [x, h]=2h in the context of Drinfeld’s quantization program.

scholarly journals Cones from quantum groups to tropical flag varieties

2021 ◽  
Author(s):  
Xin Fang ◽  
Ghislain Fourier ◽  
Markus Reineke
Keyword(s):  
Quantum Groups ◽  
Flag Varieties ◽  
Quiver Representations ◽  
Canonical Bases ◽  
Enveloping Algebras ◽  
Quantized Enveloping Algebras

AbstractWe relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in the study of monomials in canonical bases, to K-theoretic cones for quiver representations, and to some maximal prime cones in tropical flag varieties.

Energy, Information, and Superluminal Speed in Quantum Electrodynamics

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Excited Atom ◽  
Standard Quantum ◽  
Energy Information

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.

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