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

See also

Notes

  1. Khalkhali (2009), [[[:Template:Google books]] p. 48]
  2. Dokuchaev, Exel & Piccione (2000), p. 7
  3. da Silva & Weinstein (1999), [[[:Template:Google books]] p. 97]
  4. Khalkhali & Marcolli (2008), [[[:Template:Google books]] p. 210]

References

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