Group algebra information

In mathematics, the group algebra can mean either A group ring of a group over some ring. A group algebra of a locally compact group. This disambiguation...

mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus...

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...

In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A...

elements. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined...

In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free...

quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

Heyting algebra Hopf algebra Non-associative algebra Outline of algebra Relational algebra Sigma-algebra Symmetric algebra T-algebra Tensor algebra When...

. Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds: every Lie group gives rise to a Lie algebra, which...

type of C*-algebra. Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of single operators, group representations...

In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative)...

In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)...

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...

'infinitesimal' representations of Lie algebras. A complex representation of a group is an action by a group on a finite-dimensional vector space over...

the group Hopf algebra of a given group is a certain construct related to the symmetries of group actions. Deformations of group Hopf algebras are foundational...

algebras generalize the notions of group algebras and incidence algebras, just as categories generalize the notions of groups and partially ordered sets. If...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

subalgebras include diagram algebras such as the Brauer algebra, the Temperley–Lieb algebra, or the group algebra of the symmetric group. Representations of the...

mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure...

The Hecke algebra of a finite group is the algebra spanned by the double cosets HgH of a subgroup H of a finite group G. It is a special case of a Hecke...

problems in abstract algebra to problems in linear algebra, a subject that is well understood. For instance, representing a group by an infinite-dimensional...

Genetic algebra Geometric algebra Gerstenhaber algebra Graded algebra Griess algebra Group algebra Group algebra of a locally compact group Hall algebra Hecke...

of an algebraic group is the identity component of its maximal normal solvable subgroup. For example, the radical of the general linear group GL n ⁡...

universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

group is a linear space, vectors in the Lie algebra can be canonically identified with vectors in the group. The Lie algebra of the Heisenberg group is...