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
C*-Algebra, Group Algebra, Group 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