Corach, G.; Porta, H.; Recht, L. Multiplicative integrals and geometry of spaces of projections. (English) Zbl 0756.46041 Rev. Unión Mat. Argent. 34(1990), 132-149 (1988). Let \(A\) be a Banach algebra with 1 (over \(\mathbb{R}\) or \(\mathbb{C}\)) and \[ Q_ n=\{q=(q_ 1,\dots,q_ n)\in A^ n:\;q_ k^ 2=q_ k,\;q_ i q_ k=0\text{ if } i\neq k,\;\sum q_ k^ 2=1\}. \] For \(q_ 0\in Q_ n\) the map \(\pi: G\to Q_ n\), \(\pi(g)=gq_ 0g^{-1}\) (\(G\) stands for the group of units of \(A\)) defines a principal fiber bundle over its image. For a “good” curve \(\gamma: [0,1]\to Q_ n\) with origin \(q_ 0\) the authors construct an explicit lift which turns out to be the horizontal lift of \(\gamma\) with respect to the natural connection. A similar result is given for the space \[ S_ q=\{(a,b)\in A^ 2:\;aq=a,\;qb=b,\;ba=q\}, \] where \(q\in A\) is a fixed idempotent. These constructions are based on the techniques of multiplicative integrals. Reviewer: A.Pankov (Vinnitsa) Cited in 5 Documents MSC: 46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) 46H05 General theory of topological algebras 53C05 Connections (general theory) Keywords:joint similarity orbit; principal fiber bundle; horizontal lift; connection; multiplicative integrals PDFBibTeX XMLCite \textit{G. Corach} et al., Rev. Unión Mat. Argent. 34, 132--149 (1988; Zbl 0756.46041)