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Groupoid algebra : ウィキペディア英語版
Groupoid algebra
In mathematics, the concept of groupoid algebra generalizes the notion of group algebra.〔Khalkhali (2009), (p. 48 )〕
== Definition ==
Given a groupoid (G, \cdot) and a field K, it is possible to define the groupoid algebra KG as the algebra over K formed by the vector space having the elements of G as generators and having the multiplication of these elements defined by g
* h = g \cdot h, whenever this product is defined, and g
* h = 0 otherwise. The product is then extended by linearity.〔Dokuchaev, Exel & Piccione (2000), p. 7〕

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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