Properly Outer and Strictly Outer Actions of Finite Groups on Prime C*-algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917635468296192 |
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| author | Peligrad, Costel |
| author_facet | Peligrad, Costel |
| contents | An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the C*-algebra. In this paper I define the notion of strictly outer action (similar to the definition for von Neumann factors in [11]) and prove that for finite groups it is equivalent with proper outerness of the action. For finite abelian groups this is equivalent with other relevant properities of the action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04232 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Properly Outer and Strictly Outer Actions of Finite Groups on Prime C*-algebras Peligrad, Costel Operator Algebras An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the C*-algebra. In this paper I define the notion of strictly outer action (similar to the definition for von Neumann factors in [11]) and prove that for finite groups it is equivalent with proper outerness of the action. For finite abelian groups this is equivalent with other relevant properities of the action. |
| title | Properly Outer and Strictly Outer Actions of Finite Groups on Prime C*-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2303.04232 |