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

Katsunori Kawamura

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

Operator Algebras 2009-12-21 v1 Quantum Algebra

Authors: Katsunori Kawamura

Abstract

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.

Keywords

C*-bialgebra universal R-matrix comultiplication multiplier algebra intertwiner quantum group

Cite

@article{arxiv.0912.3578,
  title  = {Non-existence of universal $R$-matrix for some C$^{*}$-bialgebras},
  author = {Katsunori Kawamura},
  journal= {arXiv preprint arXiv:0912.3578},
  year   = {2009}
}

Comments

8 pages

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