2014/11/12 by Ingrid Beltiţă, Beltita, Ingrid, Daniel Beltiţă +3 · 1 citation
Mathematics · #22E25 #46L35 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Primary 43A30 #Representation Theory (math.RT) #Secondary 22E27
paper · pdf · doi:10.48550/arxiv.1411.3254
openalex publication_date 2014/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any nilpotent Lie group G we provide a description of the image of its C^*-algebra through its operator-valued Fourier transform. Specifically, we show that C^*(G) admits a finite composition series such that that the spectra of the corresponding quotients are Hausdorff sets in the relative topology, defined in terms of the fine stratification of the space of coadjoint orbits of G, and the canonical fields of elementary C^*-algebras defined by the successive subquotients are trivial. We give a description of the image of the Fourier transform as a C^*-algebra of piecewise continuous operator fields on the spectrum, determined by the boundary behavior of the restrictions of operator fields to the spectra of the subquotients in the composition series. For uncountable families of 3-step nilpotent Lie groups and also for a sequence of nilpotent Lie groups of arbitrarily high nilpotency step, we prove that every continuous trace subquotient of their C^*-algebras has its Dixmier-Douady invariant equal to zero.