Friday, February 4, 2011

Theory Update 55

For the ribbon braid group $B_3$, we can twist ribbons and also perform braiding within the three strands of $B_3$. One cyclic set of generators is shown.
The generators $(12,23,31)$ are those given by the trefoil quandle. The ribbon strands are labeled $1$, $2$, $3$. We see that two qutrits may be used to label the generators, under the correspondence $1 = XX$ and $12 = \{ XY , YX \}$. In other words, the three ribbons are specified by the letters $X$, $Y$ and $Z$.

Observe that the trefoil quandle rule is now naturally associated to braids of the form $\sigma_{1} \sigma_{2}^{-1} = (12)(23)^{-1}$ $= 12 3^{-1} 2^{-1}$, which are used to specify the Bilson-Thompson particle spectrum. Since qutrits and triality are used to specify braid information, a $3 \times 3$ Koide mass matrix now lives in an exceptional bioctonion Jordan algebra, as do the neutrino and CKM mixing matrices.


  1. Oh, look. Someone has discovered that the trinities are important for physics. Well, many people knew that already, but as someone points out, not many are focusing on measurement algebras. Some of us have been for many, many years, but what would we know?

    Most people can be excused for ignoring a nice thesis because they have neither heard of it nor read it. One demands some embarrassment, however, from someone who cannot claim not to have ever read said thesis, being, as they were, one of its examiners.

  2. Maybe someone has long fingers? Or very bad memory, but then his whole work is meaningless.

    Rude robbery has many times had success, giving even a Nobel prize. Maybe someone ought to point it out more clearly?

  3. Yes, the worst thing is that no one else thought to say anything.


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