Partial Group Algebra

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

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

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

• Group ring
• Group representation

• 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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