2012/08/19 by Cornel Pasnicu, Pasnicu, Cornel, N. Christopher Phillips +1 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #46L #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Neuroendocrine Tumor Research Advances #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1208.3810
openalex publication_date 2012/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an action of a finite group on a C*-algebra, we present some conditions\nunder which properties of the C*-algebra pass to the crossed product or the\nfixed point algebra. We mostly consider the ideal property, the projection\nproperty, topological dimension zero, and pure infiniteness. In many of our\nresults, additional conditions are necessary on the group, the algebra, or the\naction. Sometimes the action must be strongly pointwise outer, and in a few\nresults it must have the Rokhlin property. When the group is finite abelian, we\nprove that crossed products and fixed point algebras preserve topological\ndimension zero with no condition on the action.\n We give an example to show that the ideal property and the projection\nproperty do not pass to fixed point algebras (even for the two element group).\nThe construction also gives an example of a C*-algebra which does not have the\nideal property but such that the algebra of 2 by 2 matrices over it does have\nthe ideal property; in fact, this matrix algebra has the projection property.\n