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We prove a number of results having to do with equipping type-I\mathrm{C}^*-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the\mathrm{C}^*-algebra in question is an extension of a non-zero finite direct sum of elementary\mathrm{C}^*-algebras by a commutative unital\mathrm{C}^*-algebra then it must be finite-dimensional.
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This content will become publicly available on June 16, 2026
Crossed products and $\mathrm{C}^{*}$-covers of semi-Dirichlet operator algebras
In this paper, we show that the semi-Dirichlet\mathrm{C}^{*}-covers of a semi-Dirichlet operator algebra form a complete lattice, establishing that there is a maximal semi-Dirichlet\mathrm{C}^{*}-cover. Given an operator algebra dynamical system we prove a dilation theory that shows that the full crossed product is isomorphic to the relative full crossed product with respect to this maximal semi-Dirichlet cover. In this way, we can show that every semi-Dirichlet dynamical system has a semi-Dirichlet full crossed product.
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- Award ID(s):
- 2054781
- PAR ID:
- 10627845
- Editor(s):
- Winter, W
- Publisher / Repository:
- EMS
- Date Published:
- Journal Name:
- Documenta Mathematica
- Volume:
- 30
- Issue:
- 4
- ISSN:
- 1431-0635
- Page Range / eLocation ID:
- 909 to 933
- Subject(s) / Keyword(s):
- Crossed product operator algebra
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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