Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbers

Details Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbers Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbers

2009-04-28

arxiv.org/abs/0904.4296v1

Mathematics

Operator Algebras

15 pages

Scientific paper

Let ${\cal O}_{*}$ be the C$^{*}$-algebra defined as the direct sum of all Cuntz algebras. Then ${\cal O}_{*}$ has a non-cocommutative comultiplication $\Delta_{\phi}$ and a counit $\epsilon$. Let ${\rm BI}({\cal O}_{*})$ denote the set of all closed biideals of the C$^{*}$-bialgebra $({\cal O}_{*},\Delta_{\phi},\epsilon)$ 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 ${\cal P}({\bf P})$.

Affiliated with

Also associated with

No associations

Rating

Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Biideals and a lattice of C$^{*}$-bialgebras associated with prime numbers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-712729