Le Groupe Quantique Compact Libre U(n)

The free analogues of U(n) in Woronowicz' theory [Wo2] are the compact matrix quantum groups introduced by Wang and Van Daele. We classify here their irreducible representations. Their fusion rules turn to be related to the combinatorics of Voiculescu's circular variable. If we find an embedding , where A _o (F) is the deformation of SU(2) studied in [B2]. We use the representation theory and Powers' method for showing that the reduced algebras A _u (F) _red are simple, with at most one trace. Received: 1 March 1996 / Accepted: 4 April 1997     

可溶性汞化苯乙烯－丙烯酸甲酯共聚物的合成

用自由基溶液降合方法制备一系列苯乙烯－丙烯酸甲酯线型共聚物，用核磁共振测定了苯基在共聚物中的百分比，在该共聚物的四氢呋喃溶液中，用三氟乙酸汞在共聚物的苯环上进行亲电取代反应，得到可溶性汞化共聚物，由于这类泵化共的可溶于四氢呋喃，二氯甲烷等溶剂，用重沉淀法多次提纯，得到了纯度很高，溶解性较好的含重金属二价汞的共聚物，用红外光谱仪测定共聚物上的汞基团，用原子吸收定量测试共聚中的汞的百分聚代率，结果表明     

Catalytic cathodic stripping voltammetry of oxidized glutathione at a hanging mercury drop electrode in the presence of nickel ion

Oxidized glutathione (GSSG) can be determined after previous accumulation on the HMDE at E > -0.2 V (vs. the Ag AgCl reference electrode). GSH is formed during the accumulation, possibly by a mercury-ion-assisted hydrolytic disproportionation of GSSG. In the subsequent cathodic scan GSH is released and catalyses the reduction of nickel ion, giving a peak located at -0.6 V. This enables the determination of GSSG by differential-pulse cathodic stripping voltammetry at pH 7.0 in the phosphate acetate or MOPS buffer containing 0.5-1.0 mM Ni(II). The detection limit is 10 nM. The calibration graph is linear even in the presence of small amounts of human serum albumin, HSA. However, HSA increases the detection limit (20 nM for 3 x 10(-4)% HSA). Acetyl-cysteine in small excess or Cu(II) present as reagent impurity do not interfere. Glutathione, cysteine and similar compounds, which accumulate as mercury salts and form stable nickel complexes, will interfere. The method is put forward as a novel alternative stripping voltammetric method to those involving accumulation and determination as mercury or copper salts and complexes, in the knowledge that it may have advantages in particular analytical situations. In particular the method discriminates against compounds which accumulate as mercury salts but which do not form stable nickel complexes.     

Symmetries of a generic coaction

If B is -algebra of dimension $4\leq n<\infty$ then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say , have the same fusion rules as the ones of SO(3). As consequences, we get (1) a structure result for in the case where B is a matrix algebra (2) if then the dual is not amenable (3) if then the fixed point subfactor has index n and principal graph . Received: 3 December 1998 / in final form: 8 January 1999     

Quantum automorphism groups of vertex-transitive graphs of order ≤ 11

We study quantum automorphism groups of vertex-transitive graphs having less than 11 vertices. With one possible exception, these can be obtained from cyclic groups , symmetric groups S _n and quantum symmetric groups , by using various product operations. The exceptional case is that of the Petersen graph, and we present some questions about it.     

On the classification of complex vector bundles of stable rank

One describes, using a detailed analysis of Atiyah-Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constructive terms the Chern classes of a vector bundle. Since deceased.