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arXiv · 1109.2962

C$^{*}$-bialgebra defined as the direct sum of UHF algebras

Katsunori Kawamura
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Abstract

Let ${\cal A}_{0}(*)$ denote the direct sum of a certain set of UHF algebras and let ${\cal A}(*)\equiv {\bf C}\oplus {\cal A}_{0}(*)$. We introduce a non-cocommutative comultiplication $Δ_ϕ$ on ${\cal A}(*)$, and give an example of comodule-C$^{*}$-algebra of the C$^{*}$-bialgebra $({\cal A}(*),Δ_ϕ)$. With respect to $Δ_ϕ$, we define a non-symmetric tensor product of *-representations of UHF algebras and show tensor product formulas of GNS representations by product states.

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BibTeXRIS

Katsunori Kawamura. 2011-09-14. C$^{*}$-bialgebra defined as the direct sum of UHF algebras. https://arxiv.org/abs/1109.2962

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