On the Absence of Continuous Symmetries for Noncommutative 3-Spheres
نویسندگان
چکیده
A large class of noncommutative spherical manifolds was obtained recently from cohomology considerations. A one-parameter family of twisted 3-spheres was discovered by Connes and Landi, and later generalized to a three-parameter family by Connes and Dubois-Violette. The spheres of Connes and Landi were shown to be homogeneous spaces for certain compact quantum groups. Here we investigate whether this property can be extended to the noncommutative three-spheres of Connes and Dubois-Violette. Upon restricting to quantum groups which are continuous deformations of Spin(4) and SO(4) with standard co-actions, our results suggest that this is not the case.
منابع مشابه
Equivariant noncommutative index on braided sphere
To some Hecke symmetries (i.e. Yang-Baxter braidings of Hecke type) we associate ”noncommutative varieties” called braided spheres. An example of such a variety is the Podles’ nonstandard quantum sphere. On any braided sphere we introduce and compute an ”equivariant” analogue of Connes’ noncommutative index. In contrast with the Connes’ construction our version of equivariant NC index is based ...
متن کاملSpin-Hall effect with quantum group symmetries
We construct a model of spin-Hall effect on a noncommutative four sphere S4 θ with isospin degrees of freedom, coming from a noncommutative instanton, and invariance under a quantum group SOθ(5). The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on highe...
متن کاملNoncommutative Balls and Mirror Quantum Spheres
Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the ‘even-dimensional’ case they correspond to the Twisted Canonical Commutation Relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C-algebras and polynomial algebras...
متن کاملA note on power values of generalized derivation in prime ring and noncommutative Banach algebras
Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $ngeq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,yin R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.
متن کاملSetting Hidden Symmetries Free by the Noncommutative Veronese Mapping
The note is devoted to the setting free of hidden symmetries in Verma modules over sl(2, C) by the noncommutative Veronese mappings. In many cases the behavior of systems is governed not only by their natural (geometric) symmetries but also by hidden ones. The main difficulty to work with hidden symmetries is that they are often ”packed”, and as a rule can’t be ”unpacked” to the universal envel...
متن کامل