We construct ergodic actions of compact quantum groups on C∗-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups. In particular, we construct: (1). an ergodic action of the compact quantum Au(Q) on the type IIIλ Powers factor Rλ for an appropriate positive Q ∈ GL(2, R); (2). an ergodic action of the compact...

In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In §1 we prove that Loeb spaces are compact under various assumptions, and in §2 we prove that Loeb spaces are not compact under various other assumptions. The results in §1 and §2 give a quite complete answer to a quest...

$P_c$ resonances are studied in the approach of quark model and group theory. It is found that there totally 17 possible pentaquark states with contents $q^3Q \bar Q$ ($q$ $u$ $d$ quarks; $Q$ $c$ quark) compact picture, where hidden heavy may take color singlet-singlet ($[111]_{{qqq}}\otimes [111]_{{c c}}$) octet-octet ($[21]_{{qqq}}\otimes [21]_{{c configurations. The partial decay widths calc...

Introduction. Let G be a Lie group and M a compact C manifold. In [2] Anosov actions of G on M are defined and proved to be structurally stable. In this announcement we are concerned with the foliation ^ of M defined by the orbits of G. Under the assumption that G is connected, # is C stable (3). If G is connected and nilpotent, G has a compact orbit (4). If G is merely solvable, however, there...

In this paper, we introduce a new notion of quadratic Killing normal Jacobi operator (simply, operator) and its geometric meaning for real hypersurfaces in the complex Grassmannians rank two G2m+2(c), c≠0. addition, give classification theorems Hopf with two-plane compact type non-compact type.