Free diffusions, free entropy and free Fisher information
Free dynamical quantum groups and the dynamical quantum group
We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the level of universal C*-algebras. As an example, we recover the dynamical studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.
Free generalized gamma convolutions.
Free powers of the free Poisson measure
We compute moments of the measures , where ϖ denotes the free Poisson law, and ⊞ and ⊠ are the additive and multiplicative free convolutions. These moments are expressed in terms of the Fuss-Narayana numbers.
Free probability theory and non-crossing partitions.
Freeness with amalgamation, limit theorems and S-transform in non-commutative probability spaces of type B
The paper addresses several problems left open by P. Biane, F. Goodman and A. Nica [Trans. Amer. Math. Soc. 355 (2003)]. The main result is that a type B non-commutative probability space can be studied in the framework of freeness with amalgamation. This view allows easy ways of constructing a version of the S-transform as well as proving analogues to the Central Limit Theorem and Poisson Limit Theorem.
From double Lie groups to quantum groups
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
Functional calculus and spectral theory of locally C*-sums of locally m-convex C*-algebras
Fusion en algèbres de von Neumann et groupes de lacets
Fuss-Catalan numbers in noncommutative probability.
Gabor Time-Frequency Lattices and the Wexler-Raz Identity.
GAGA for DQ-algebroids
Gauss polynomials and the rotation algebra.
Gaussian random band matrices and operator-valued free probability theory
Generalized derivations and -algebras.
Generalized inverses in C*-algebras II
Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.
Generalized Jensen's equations in Banach modules over a unital -algebra.
Generalized non-commutative tori
The generalized non-commutative torus of rank n is defined by the crossed product , where the actions of ℤ on the fibre of a rational rotation algebra are trivial, and is a non-commutative torus . It is shown that is strongly Morita equivalent to , and that is isomorphic to if and only if the set of prime factors of k is a subset of the set of prime factors of p.
Generalized q-deformed Gaussian random variables
We produce generalized q-Gaussian random variables which have two parameters of deformation. One of them is, of course, q as for the usual q-deformation. We also investigate the corresponding Wick formulas, which will be described by some joint statistics on pair partitions.
Generalized stability of -ternary quadratic mappings.