Lévy Processes on Quantum Groups and Dual Groups

2005 ◽  
pp. 161-257 ◽  
Author(s):  
Uwe Franz
Keyword(s):  
Quantum Groups ◽  
Lévy Processes ◽  
Levy Processes ◽  
Dual Groups

Quantum Lévy processes on dual groups

2005 ◽  
Vol 251 (1) ◽  
pp. 147-165 ◽  
Author(s):  
Anis Ben Ghorbal ◽  
Michael Schürmann
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Dual Groups

scholarly journals Lévy–Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups

2018 ◽  
Vol 21 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Biswarup Das ◽  
Uwe Franz ◽  
Anna Kula ◽  
Adam Skalski
Keyword(s):  
Quantum Groups ◽  
Cohomology Group ◽  
Lévy Processes ◽  
Levy Processes ◽  
Degenerate Case ◽  
Cohomology Groups ◽  
Compact Quantum Groups

We study the first and second cohomology groups of the [Formula: see text]-algebras of the universal unitary and orthogonal quantum groups [Formula: see text] and [Formula: see text]. This provides valuable information for constructing and classifying Lévy processes on these quantum groups, as pointed out by Schürmann. In the case when all eigenvalues of [Formula: see text] are distinct, we show that these [Formula: see text]-algebras have the properties (GC), (NC) and (LK) introduced by Schürmann and studied recently by Franz, Gerhold and Thom. In the degenerate case [Formula: see text], we show that they do not have any of these properties. We also compute the second cohomology group of [Formula: see text] with trivial coefficients — [Formula: see text] — and construct an explicit basis for the corresponding second cohomology group for [Formula: see text] (whose dimension was known earlier, thanks to the work of Collins, Härtel and Thom).

On correlating Lévy processes

2010 ◽  
Vol 13 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Ernst Eberlein ◽  
Dilip Madan
Keyword(s):  
Lévy Processes ◽  
Levy Processes
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