Algebry operatorów i ich zastosowania w fizyce

A locally compact quantum group with projection is a quantum counterpart of a semidirect product of groups. Such a group is a (trivial) extension of the image of the projection by the kernel of the projection. For a quantum group with a projection to be extension of the image of the projection a certain additional condition must be satisfied. We shall describe the following examples: U_q(2), quantum az+b groups and the dual of a classical group with projection . It will be shown that U_q(2) is an extension of one dimensional torus if and only if q is real and then U_q(2) is extension of one dimensional torus by SUq(2). Quantum 'az+b' is an extension of the image of the projection if and only if it is classical group. Finally the dual of a classical group is an extension of the dual of the image of the projection if and only if the group is a Cartesian product. This is joint work with P. Sołtan.The seminars take place in room 2.23 at the Physics Department, Pasteura 5 (II p.)P. Kasprzak, P.M. Sołtan, W Pusz.

A locally compact quantum group with projection is a quantum counterpart of a semidirect product of groups. Such a group is a (trivial) extension of the image of the projection by the kernel of the projection. For a quantum group with a projection to be extension of the image of the projection a certain additional condition must be satisfied. We shall describe the following examples: U_q(2), quantum az+b groups and the dual of a classical group with projection . It will be shown that U_q(2) is an extension of one dimensional torus if and only if q is real and then U_q(2) is extension of one dimensional torus by SUq(2). Quantum 'az+b' is an extension of the image of the projection if and only if it is classical group. Finally the dual of a classical group is an extension of the dual of the image of the projection if and only if the group is a Cartesian product. This is joint work with P. Sołtan.