2025/02/06 by A. A. Rakhimov, Rakhimov, A. A., Laylo Ramazonova +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2502.04137
It is shown that every outer *-automorphism of a real C*-algebra can be uniquely extended to an injective envelope of real C*-algebra. It is proven that if a real C*-algebra is a simple, then its injective envelope is also simple, and it is a real AW*-factor. The example of a real C*-algebra that is not real AW*-algebra and the injective envelope is a real AW*-factor of type III, which is not a real W*-algebra is constructed. This leads to the interesting result that up to isomorphism, the class of injective real (resp. complex) AW*-factors of type III is at least one larger than the class injective real (resp. complex) W*-factors of type III.