Localization of fringes in speckle photography that are due to axial motion of the diffuse object (original) (raw)
1988, Journal of the Optical Society of America A
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2020
We summarize the definition of the Weyl groupoid using supercategory approach in order to investigate quantum superalgebras at roots of unity. We show how the structure of a Hopf superalgebra on a quantum superalgebra is determined by the quantum Weyl groupoid. The Weyl groupoid of mathfraksl(m∣n)\mathfrak{sl}(m|n)mathfraksl(m∣n) is constructed to this end as some supercategory. We prove that in this case quantum superalgebras associated with Dynkin diagrams are isomorphic as superalgebras. It is shown how these quantum superalgebras considered as Hopf superalgebras are connected via twists and isomorphisms. We explicitly construct these twists using the Lusztig isomorphisms considered as elements of the Weyl quantum groupoid. We build a PBW basis for each quantum superalgebra, and investigate how quantum superalgebras are connected with their classical limits, i. e. Lie superbialgebras. We find explicit multiplicative formulas for universal RRR-matrices, describe relations between them for each realization an...
Twist deformations of the supersymmetric quantum
2011
TheN -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For evenN one can identify the 1DN -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main dierences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.
Weyl groupoid of quantum superalgebra sl(2|1) at roots of unity
2020
We summarize the definition of the Weyl groupoid in order to investigate quantum superalgebras. The Weyl groupoid of sl(2|1) is constructed to this end. We prove that in this case quantum superalgebras associated with Dynkin diagrams are isomorphic as superalgebras. It is shown how these quantum superalgebras considered as Hopf superalgebras are connected via twists and isomorphisms. We build a PBW basis for each quantum superalgebra, and investigate how quantum superalgebras are connected with their classical limits, i. e. Lie superbialgebras. We find explicit multiplicative formulas for universal R-matrices and describe relations between them for each realization.
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