# Groupoid algebra

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In mathematics, the concept of **groupoid algebra** generalizes the notion of group algebra.^{[1]}

## Definition

Given a groupoid and a field , it is possible to define the groupoid algebra as the algebra over formed by the vector space having the elements of as generators and having the multiplication of these elements defined by , whenever this product is defined, and otherwise. The product is then extended by linearity.^{[2]}

## Examples

Some examples of groupoid algebras are the following:^{[3]}

## Properties

- When a groupoid has a finite number of objects and a finite number of morphisms, the groupoid algebra is a direct sum of tensor products of group algebras and matrix algebras.
^{[4]}

## See also

## Notes

## References

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