representation, ∞-representation?
symmetric monoidal (∞,1)-category of spectra
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
Let $k$ be a commutative unital ring, $(C,\Delta)$ a (counital) $k$-coalgebra and $(A,m)$ an associative (unital) $k$-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 $f,g$ is given by
Given a finite group $G$ and a ring $R$, the space of functions $C(G,R)$ inherits the convolution product defined by
This is the non-commutative product operation that appears in the Hopf algebra structure on $C(G,R)$.
More generally, there is convolution of functions on morphisms of a groupoid. See at groupoid convolution algebra for details.
Last revised on April 5, 2013 at 18:54:19. See the history of this page for a list of all contributions to it.