The Calkin algebra is not countably homogeneous Academic Article uri icon

abstract

  • PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 144, Number 12, December 2016, Pages 5351–5357 http://dx.doi.org/10.1090/proc/13137 Article electronically published on May 23, 2016 … THE CALKIN ALGEBRA IS NOT COUNTABLY HOMOGENEOUS … Abstract. We show that the Calkin algebra is not countably homogeneous, in the sense of continuous model theory. We furthermore show that the con- nected component of the unitary group of the Calkin algebra is not countably homogeneous … Motivated by their study of extensions of C … Fillmore asked whether the Calkin algebra has a K-theory reversing automorphism and whether it has outer automorphisms at all ([4, Remark 1.6 (ii)]). By [16] and [8] the answer to the latter question is independent from ZFC. In particular, since inner automorphisms fix K-theory, a negative answer to the former question is relatively consistent with ZFC. It is not known whether …

publication date

  • January 1, 2016