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

Abstract

For a C${}^{\ast }$-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${}^{\ast }$-bialgebras.

arXiv comment8 pages

References in corpus (1)

• Biideals and a lattice of C${}^{\ast }$-bialgebras associated with prime numbers

Cited by in corpus (3)

• Triangular C${}^{\ast }$-bialgebra defined as the direct sum of matrix algebras
• $R$-matrices and the Yang-Baxter equation on GNS representations of C${}^{\ast }$-bialgebras
• Inductive limit violates quasi-cocommutativity