Partial group algebra

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

Examples

• The partial group algebra $\mathbb {C} _{\text{par}}(\mathbb {Z} _{4})$ is isomorphic to the direct sum:

  $\mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathrm {M} _{2}\mathbb {C} \oplus \mathrm {M} _{3}\mathbb {C}$

See also

• Group ring
• Group representation

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.