Groupoid algebra
In mathematics, the concept of groupoid algebra generalizes the notion of group algebra. == Definition == Given a groupoid ( G , ⋅ ) {\displaystyle (G,\cdot )} (in the sense of a category with all morphisms invertible) and a field K {\displaystyle K} , it is possible to define the groupoid algebra K G {\displaystyle KG} as the algebra over K {\displaystyle K} formed by the vector space having the elements of (the morphisms of) G {\displaystyle G} as generators and having the multiplication of these elements defined by g ∗ h = g ⋅ h {\displaystyle g*h=g\cdot h} , whenever this product is defined, and g ∗ h = 0 {\displaystyle g*h=0} otherwise.