Partial group algebra

A partial group algebra is an associative algebra related to the partial representations of a group.

Examples

• The partial group algebra $\mathbb{C}_{\text{par}}\left(\mathbb{Z}_4\right)$ is isomorphic to the direct sum:^[1]

  $\mathbb{C}\oplus \mathbb{C}\oplus\mathbb{C}\oplus\mathbb{C}\oplus\mathbb{C}\oplus\mathbb{C}\oplus\mathbb{C}\oplus M_2\left(\mathbb{C}\right) \oplus M_3\left(\mathbb{C}\right)$

See also

• Group algebra
• Group representation

Notes

1. R. Exel (1998)

References

• R. Exel. Partial Actions of Groups and Actions of Semigroups. Proc. Am. Math. Soc. 126 no. 12 (1998), 3481–3494.