In mathematics, a partial group algebra is an associative algebra related to the partial representations of a group.

Examples

• The partial group algebra ${\displaystyle \mathbb {C} _{\text{par}}\left(\mathbb {Z} _{4}\right)}$ is isomorphic to the direct sum:^[1]

  ${\displaystyle \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus M_{2}\left(\mathbb {C} \right)\oplus M_{3}\left(\mathbb {C} \right)}$

See also

• Group ring
• Group representation

Notes

References

• Exel, Ruy (1998). "Partial Actions of Groups and Actions of Inverse Semigroups". Proceedings of the American Mathematical Society. 126 (12): 3481–3494. doi:10.1090/S0002-9939-98-04575-4.