Re: Why is there no *really* useful Algebra beyond complex numbers? (and if it were, would John Baez talk about it?)

Sorry- I was writing as a myopic engineer! I should have said "many",
not "most"; many Banach algebras are Hoops. I made a worse error in
writing "seminorm", which implies non-negativity. Quadratic conserved
properties ("sizes" herafter) can be negative. "Study numbers" x + k y
live on the hyperbolic plane, with k^2=1 but k not= -1. Their dual is
(u,phi) with u^2 = x^2-y^2 (I call u an ulna) and phi = ArcTanh[x,y]
(taking the octant into account). Until I checked the definition, I
called u a seminorm. Does it have a recognised name? Some sizes look
like Planck areas; in the Pauli-sigma example the points outside the
light-cone have a negative size.
Roger Beresford.
"If we do not find anything pleasant, at least we shall find something
new." (Voltaire)

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