Non-existence of universal $R$-matrix for some C$^{*}$-bialgebras

Details Non-existence of universal $R$-matrix for some C$^{*}$-bialgebras Non-existence of universal $R$-matrix for some C$^{*}$-bialgebras

2009-12-18

arxiv.org/abs/0912.3578v1

Mathematics

Operator Algebras

8 pages

Scientific paper

For a C$^{*}$-bialgebra $A$ with a comultiplication $\Delta$, a universal
$R$-matrix of $(A,\Delta)$ is defined as a unitary element in the multiplier
algebra $M(A\otimes A)$ of $A\otimes A$ which is an intertwiner between
$\Delta$ and its opposite comultiplication $\Delta^{op}$. We show that there
exists no universal $R$-matrix for some C$^{*}$-bialgebras.

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