Emails from Roland
August 23, 2017
10:58 PM
Dear Dror,
I believe normal ordering will yield a topology on our yax algebra and doubles in general.
Referring to the presentation of the U_{h;\alpha,\beta} algebra on your monoblog,
set h = \alpha =1, we dont need them.
Now consider the algebra U generated by y,a,x,\beta,T.
We can (and do) order every monomial in the standard order y,a,x,\beta,T.
This extends to a linear bijection O: Q[[Y,A,X,B,T]] ---> U
sending                                   Y^kA^lX^mB^nT^o to y^ka^lx^m\beta^nT^o
The map O introduces the usual topology on the power-series ring into U.
That should do it, or am I missing something?
Best,
Roland
Dear Dror,
I found a pleasing algebra automorphism Phi which in the U_{h,\alpha,\beta} conventions of the monoblog reads:
Phi(x) = -A^{-1} y
Phi(y) = -B^{-1} x
Phi(a) = -a
Phi(b) = -b
Enjoy Switzerland.
Best,
Roland