Outer actions of finite groups on prime C*-algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913593001246720 |
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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 and strictly outer if the commutant of the algebra in the algebra of local mutipliers of the cross product consists of scalars [11]. In [11, Theorem 11] I proved that for finite groups and prime C*-algebras (not necessarily separable), the two notions are equivalent. I also proved that for finite abelian groups this is equivalent to other relevant properties of the action [11 Theorem 14]. In this paper I add other properties to the list in [11, Theorem 14]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 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 and strictly outer if the commutant of the algebra in the algebra of local mutipliers of the cross product consists of scalars [11]. In [11, Theorem 11] I proved that for finite groups and prime C*-algebras (not necessarily separable), the two notions are equivalent. I also proved that for finite abelian groups this is equivalent to other relevant properties of the action [11 Theorem 14]. In this paper I add other properties to the list in [11, Theorem 14]. |
| title | Outer actions of finite groups on prime C*-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2408.02510 |