C$^{*}$-bialgebra defined by the direct sum of Cuntz algebras

Details C$^{*}$-bialgebra defined by the direct sum of Cuntz algebras C$^{*}$-bialgebra defined by the direct sum of Cuntz algebras

2007-02-13

arxiv.org/abs/math/0702355v3

Mathematics

Operator Algebras

18 pages

Scientific paper

We show that a tensor product among representation of certain C$^{*}$-algebras induces a bialgebra. Let $\tilde{{\cal O}}_{*}$ be the smallest unitization of the direct sum of Cuntz algebras \[{\cal O}_{*}\equiv {\bf C}\oplus {\cal O}_{2}\oplus {\cal O}_{3}\oplus{\cal O}_{4}\oplus ....\] We show that there exists a non-cocommutative comultiplication $\Delta$ and a counit $\epsilon$ of $\tilde{{\cal O}}_{*}$. From $\Delta,\vep$ and the standard algebraic structure, $\tilde{{\cal O}}_{*}$ is a C$^{*}$-bialgebra. Furthermore we show the following: (i) The antipode on $\tilde{{\cal O}}_{*}$ never exist. (ii) There exists a unique Haar state on $\tilde{{\cal O}}_{*}$. (iii) For a certain one-parameter bialgebra automorphism group of $\tilde{{\cal O}}_{*}$, a KMS state on $\tilde{{\cal O}}_{*}$ exists.

Affiliated with

Also associated with

No associations

Rating

C$^{*}$-bialgebra defined by the direct sum of Cuntz algebras 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 C$^{*}$-bialgebra defined by the direct sum of Cuntz algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and C$^{*}$-bialgebra defined by the direct sum of Cuntz algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-409732