A Note on Free Quantum Groups

Teodor Banica

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$L_{\infty}$ -Khintchine-Bonami inequality in free probability

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We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length ( $f = \sum_{| w | = l} a_{w} \otimes λ (w)$ ). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.

A $q$ -analogue of the centralizer construction and skew representations of the quantum affine algebra.

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The notion of a $J^{3}$ -triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements....

Almost free splitters

Rüdiger Göbel, Saharon Shelah (1999)

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Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that $E x t_{R} (G, G) = 0$ . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which...

PBW and duality theorems for quantum groups and quantum current algebras.

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$T$ -systems and $Y$ -systems for quantum affinizations of quantum Kac-Moody algebras.

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$q$ -analog of Gelfand-Graev basis for the noncompact quantum algebra $U_{q} (u (n, 1))$ .

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Dynamical $ℛ$ matrices of elliptic quantum groups and connection matrices for the $q$ -KZ equations.

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Test elements and test rank of a free metabelian group.

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Differential calculus on 'non-standard' (h-deformed) Minkowski spaces

José de Azcárraga, Francisco Rodenas (1997)

Banach Center Publications

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The differential calculus on 'non-standard' h-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.