Algebras and modules
Model category presentations
Geometry on formal duals of algebras
There are many related constructions of algebras, topological algebras and so on which bear the name of a convolution algebra.
The basic mechanism is usually the
The probably most widespread example of this is the
This is a special case of the
Of maps from a coalgebra to an algebra
Let be a commutative unital ring, a (counital) -coalgebra and an associative (unital) -algebra. Then the set of linear maps
has a structure of an associative (unital) algebra, called convolution algebra, in which the product of two linear maps is given by
Of a group
Given a finite group and a ring , the space of functions inherits the convolution product defined by
This is the non-commutative product operation that appears in the Hopf algebra structure on .
Of a groupoid/category
More generally, there is convolution of functions on morphisms of a groupoid. See at groupoid convolution algebra for details.
Revised on April 5, 2013 18:54:19
by Urs Schreiber