Group Algebras for Groups which are not Locally Compact
| dc.creator | Grundling, Hendrik | |
| dc.date | 2004-04-02 | |
| dc.date | 2004-06-04 | |
| dc.date.accessioned | 2026-07-07T05:06:59Z | |
| dc.date.available | 2026-07-07T05:06:59Z | |
| dc.description | We generalise the definition of a group algebra so that it makes sense for non-locally compact topological groups, in particular, we require that the representation theory of the group algebra is isomorphic (in the sense of Gelfand-Raikov) to the continuous representation theory of the group, or to some other important subset of representations. We prove that a group algebra if it exists, is always unique up to isomorphism. From examples, group algebras do not always exist for non-locally compact groups, but they do exist for some. We define a convolution on the dual of the Fourier-Stieltjes algebra making it into a Banach *-algebra, we prove that a group algebra if it exists, can always be embedded in this convolution algebra, and we find sufficient conditions for a subalgebra to be a group algebra. When the group is locally compact, we obtain a new characterisation of its group algebra which does not involve the Haar measure, nor behaviour of measures on compact sets. | |
| dc.description | Plain TEX, 47 pages. A theorem was added, stating that the norm on the convolution algebra J(R)* is in fact a C*-norm | |
| dc.identifier | https://arxiv.org/abs/math/0404020 | |
| dc.identifier | http://arxiv.org/abs/math/0404020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70683 | |
| dc.subject | Operator Algebras | |
| dc.subject | Mathematical Physics | |
| dc.subject | Group Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 43A10, 43A20, 43A35, 46L05 | |
| dc.title | Group Algebras for Groups which are not Locally Compact | |
| dc.type | text |