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. Disambiguation icon. |
The group algebra K[G] , where K is a field and G a group with the operation * , is the set of all linear combinations of finitely many elements of G ... |
In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) |
The group algebra of a group G G over a ring R R is the associative algebra whose elements are formal linear combinations over R R of the elements of G G and ... |
29 апр. 2012 г. · The group algebra of a group G over a field K is the associative algebra over K whose elements are all possible finite sums of the type ∑g∈Gαgg, ... |
The set (F[G],+,×) is a ring and is an F-vector space of dimension |G| with scalar multiplication compatible with group operation. Hence F[G] is an F-algebra. |
Now let X = G. G acts on G by g · h = gh. Then FG is called the group algebra of G: FG is on the one hand a vector space and on the other hand a ring (see ... |
5 мар. 2022 г. · A group is a set S with an operation ∘:S×S→S satisfying the following properties: An essential notion in mathematics is abstraction. |
In maths, a group is the combination of a set and binary operation. For example, the set of integers with an addition operation forms a group and a set of real ... |
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