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We define an operator α on ℂ³ ⊗ ℂ³ associated with the quantum group $U_{q} (2)$ , which satisfies the Yang-Baxter equation and a cubic equation (α² - 1)(α + q²) = 0. This operator can be extended to a family of operators $h_{j} : = I_{j} \otimes α \otimes I_{n - 2 - j}$ on ${(ℂ ³)}^{\otimes n}$ with 0 ≤ j ≤ n - 2. These operators generate the cubic Hecke algebra $ℋ_{q, n} (2)$ associated with the quantum group $U_{q} (2)$ . The purpose of this note is to present the construction.

On a decomposition of a von Neumann algebra

A. B. Thaheem (1981)

Rendiconti del Seminario Matematico della Università di Padova

On a Dimension for a Class of Homeomorphism Groups.

Wolfgang Krieger (1980)

Mathematische Annalen

On a generalization of W*-modules

David P. Blecher, Jon E. Kraus (2010)

Banach Center Publications

a recent paper of the first author and Kashyap, a new class of Banach modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize Hilbert spaces. In the present paper, we describe these modules, giving some motivation, and we prove several new results about them.

On a pair of automorphisms of $C^{*}$ -algebras

F. S. Cater, A. B. Thaheem (1996)

Rendiconti del Seminario Matematico della Università di Padova

On a problem of commutativity of automorphisms.

Chaudhry, M.Anwar, Thaheem, A.B. (1998)

International Journal of Mathematics and Mathematical Sciences

On a Problem of R.V. Kadison on Maximal Abelian *-Subalgebras in Factors.

Sorin Popa (1981/1982)

Inventiones mathematicae

On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions

Florent Benaych-Georges (2010)

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko–Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.

On a Teichmüller functor between the categories of complex tori and the Effros-Shen algebras.

Nikolaev, Igor V. (2009)

The New York Journal of Mathematics [electronic only]

On analytic torsion over C*-algebras

Alan Carey, Varghese Mathai, Alexander Mishchenko (1999)

Banach Center Publications

In this paper, we present an analytic definition for the relative torsion for flat C*-algebra bundles over a compact manifold. The advantage of such a relative torsion is that it is defined without any hypotheses on the flat C*-algebra bundle. In the case where the flat C*-algebra bundle is of determinant class, we relate it easily to the L^2 torsion as defined in [7],[5].

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$O^{*}$ -Topologies on the Test Function Algebra

Of-groups of crossed products by groups acting on trees.

On $0 - 1$ measure for projectors

On $0 - 1$ measure for projectors. II

On $2 \times 2$ matrices over $C^{*}$ -algebras.

On a Cauchy-Jensen functional inequality.

On a Class of KMS States for the Unitary Group U (oo).

On a cubic Hecke algebra associated with the quantum group $U_{q} (2)$