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 ${\displaystyle \mathbb {C} _{\text{par}}(\mathbb {Z} _{4})}$ is isomorphic to the direct sum:

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

See also

• Group ring
• Group representation

Notes

References

• Exel, Ruy (1998). "Partial Actions of Groups and Actions of Inverse Semigroups". Proceedings of the American Mathematical Society. 126 (12): 3481–3494. arXiv:funct-an/9511003. doi:10.1090/S0002-9939-98-04575-4.

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