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arXiv · 0906.2507

Pentagon equation arising from state equations of a C$^{*}$-bialgebra

Katsunori Kawamura
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Abstract

The direct sum ${\cal O}_{*}$ of all Cuntz algebras has a non-cocommutative comultiplication $Δ_φ$ such that there exists no antipode of any dense subbialgebra of the C$^{*}$-bialgebra $({\cal O}_{*},Δ_φ)$. From states equations of ${\cal O}_{*}$ with respect to the tensor product, we construct an operator $W$ for $({\cal O}_{*},Δ_φ)$ such that $W^{*}$ is an isometry, $W(x\otimes I)W^{*}=Δ_φ(x)$ for each $x\in {\cal O}_{*}$ and $W$ satisfies the pentagon equation.

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BibTeXRIS

Katsunori Kawamura. 2009-06-14. Pentagon equation arising from state equations of a C$^{*}$-bialgebra. https://doi.org/10.1007/s11005-010-0413-5

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