Group Algebra

In mathematics, the group algebra is any of various constructions to assign to a locally compact group an operator algebra (or more generally a Banach algebra), such that representations of the algebra are related to representations of the group. As such, they are similar to the group ring associated to a discrete group.

Read more about Group Algebra:  Group Algebras of Topological Groups: Cc(G), The Convolution Algebra L1(G), The Group C*-algebra C*(G), Von Neumann Algebras Associated To Groups

Other articles related to "groups, group, group algebra, algebra":

Maschke's Theorem - Reformulation and The Meaning
... One of the approaches to representations of finite groups is through module theory ... Representations of a group G are replaced by modules over its group algebra K ... Let G be a finite group and K a field whose characteristic does not divide the order of G ...
Faithful Representation
... In mathematics, especially in the area of abstract algebra known as representation theory, a faithful representation ρ of a group G on a vector space V is a linear ... In more abstract language, this means that the group homomorphism ρ G → GL(V) is injective ... de facto the same as -modules (with denoting the group algebra of the group G), a faithful representation of G is not necessarily a faithful module for the ...
Pontryagin Duality and The Fourier Transform - The Group Algebra
... The space of integrable functions on a locally compact abelian group G is an algebra, where multiplication is convolution if f, g are integrable functions then the ... This algebra is referred to as the Group Algebra of G ... convolution is submultiplicative with respect to the L1 norm, making L1(G) a Banach algebra ...
Group Hopf Algebra - Definition
... Let G be an arbitrary group and k a field ... The group Hopf algebra of G over k, denoted kG (or k), is as a set (and vector space) the free vector space on G over k ... As an algebra, its product is defined by linear extension of the group composition in G, with multiplicative unit the identity in G this product is also known as convolution ...
Group Algebra - Von Neumann Algebras Associated To Groups
... The group von Neumann algebra W*(G) of G is the enveloping von Neumann algebra of C*(G) ... For a discrete group G, we can consider the Hilbert space l2(G) for which G is an orthonormal basis ... Since G operates on l2(G) by permuting the basis vectors, we can identify the complex group ring CG with a subalgebra of the algebra of bounded operators on l2(G) ...

Famous quotes containing the words algebra and/or group:

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