A group 
-algebra
is a C*-algebra constructed
from a locally compact group.
For a discrete group 
, the reduced group 
-algebra is the operator-norm
closure of the complex group algebra acting on 
by the left regular representation.
The full group 
-algebra
instead completes the group algebra in the supremum
of the norms arising from all unitary
representations. There is a canonical surjection
from the full group 
-algebra onto the reduced one.
Group C^*-Algebra
See also
Baum-Connes Conjecture, C*-Algebra, Group Algebra, Group Representation, Kadison-Kaplansky Conjecture, Kaplansky's Quasitrace Conjecture, Kirchberg's Embedding Problem, Topological K-Theory, Unitary RepresentationExplore with Wolfram|Alpha
References
Blackadar, B. Operator Algebras: Theory of C*-Algebras and von Neumann Algebras. Berlin, Germany: Springer-Verlag, 2006.Cite this as:
Weisstein, Eric W. "Group C^*-Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GroupC-Star-Algebra.html