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

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

2011-09-14

arxiv.org/abs/1109.2962v1

Mathematics

Operator Algebras

21 pages. arXiv admin note: substantial text overlap with arXiv:0910.1420

Scientific paper

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 $\Delta_{\phi}$ on ${\cal A}(*)$, and give an example of comodule-C$^{*}$-algebra of the C$^{*}$-bialgebra $({\cal A}(*),\Delta_{\phi})$. With respect to $\Delta_{\phi}$, 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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