Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbers
| dc.creator | Kawamura, Katsunori | |
| dc.date | 2009-04-28 | |
| dc.date.accessioned | 2026-07-07T13:09:20Z | |
| dc.date.available | 2026-07-07T13:09:20Z | |
| dc.description | Let ${\cal O}_{*}$ be the C$^{*}$-algebra defined as the direct sum of all Cuntz algebras. Then ${\cal O}_{*}$ has a non-cocommutative comultiplication $Δ_ϕ$ and a counit $ε$. Let ${\rm BI}({\cal O}_{*})$ denote the set of all closed biideals of the C$^{*}$-bialgebra $({\cal O}_{*},Δ_ϕ,ε)$ and let ${\cal P}({\bf P})$ denote the power set of the set of all prime numbers. We show a one-to-one correspondence between ${\rm BI}({\cal O}_{*})$ and ${\cal P}({\bf P})$. Furthermore, we show that for any ${\cal I}$ in ${\rm BI}({\cal O}_{*})$, there exists a C$^{*}$-subbialgebra ${\cal B}_{\cal I}$ of ${\cal O}_{*}$ such that ${\cal O}_{*}={\cal B}_{\cal I}\oplus {\cal I}$, and the set of all such C$^{*}$-subbialgebras is a lattice with respect to the natural operations among C$^{*}$-subbialgebras, which is isomorphic to the lattice ${\cal P}({\bf P})$. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0904.4296 | |
| dc.identifier | http://arxiv.org/abs/0904.4296 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228698 | |
| dc.subject | Operator Algebras | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W30; 06B05; 11A41 | |
| dc.title | Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbers | |
| dc.type | text |