Hopf fibration in a C*‐module

Esteban Andruchow, Gustavo Corach and Lázaro Recht

Mathematische Nachrichten, 2023, vol. 296, issue 7, 2667-2690

Abstract: Let X be a right C*‐module over a unital C*‐algebra A$ {\cal A}$. We study the Hopf fibration of X: h:XP→P1(X)=projective space ofX,$$\begin{equation*} \mathfrak {h}: {\bf X} _ {\cal P} \rightarrow P1({\bf X}) = \hbox{projective space of } {\bf X} , \end{equation*}$$where the projective space of X is the set of singly generated orthocomplemented submodules of X, XP$ {\bf X} _ {\cal P}$ is the set of elements of X, which generate such submodules, and h(x)=$\mathfrak {h}({\bf x} )=$module generated by x∈XP$ {\bf x} \in {\bf X} _ {\cal P}$. The group of unitary operators of the module X acts on both spaces. We introduce a Finsler metric in XP$ {\bf X} _ {\cal P}$, which is invariant under the unitary action. Our main results establish that the map h$\mathfrak {h}$ is distance decreasing (when the projective space of X is considered with its natural unitary invariant metric), and a minimality result in XP$ {\bf X} _ {\cal P}$, characterizing metric geodesics in this space.

Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202100225

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:7:p:2667-2690

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().