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 [math]\displaystyle{ \mathbb{C}_{\text{par}}\left(\mathbb{Z}_4\right) }[/math] is isomorphic to the direct sum:^[1]

  [math]\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) }[/math]

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. 

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