• The n-Category Café Skip to the Main Content Note:These pages make extensive use of the latest XHTML and CSSStandards. • They ought to look great in any standards-compliant modern browser. • Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. • Moreover, many posts use MathML, which is, currentlyonlysupported in Mozilla. • My best suggestion (and you willthankme when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. • If that’s not possible, consider moving to the Standards-compliant and open-sourceMozillabrowser.
Article Summaries:
- John Baez is refining a mathematical description of a symmetry group that underlies the Standard Model. He and collaborator Paul Schwahn are working on a precise statement that the subgroup of the automorphism group of the Jordan algebra of self‑adjoint octonion matrices which preserves a chosen complex qutrit is exactly the subgroup that preserves any Jordan subalgebra isomorphic to (M_{3}(\mathbb{C})). Baez sketches a proof strategy: first show the subgroup preserving a standard copy of (M_{3}(\mathbb{C})) is maximal; then prove any such subalgebra can be moved to the standard copy by an automorphism. The argument relies on known transitivity of the automorphism group on Jordan frames and on results by Yokota and Faraut-Korányi.
Sources: