The C^*-algebra of the group N₇.

2024/10/07 by Ghofrane Kardi, Kardi, Ghofrane
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2410.16312

Abstract

In this paper, the C^*-algebra of the seven-dimensional un-decomposable nilpotent Lie group is characterized explicitly for the first time(see \citechin). Furthermore, the topology of its spectrum is described as a preparation for the analysis of its C^*-algebra. Then, the operator-valued Fourier transform is employed to translate the given C*-algebra into the algebra of bounded operator fields through its spectrum. We find the conditions satisfied by the image of the goal to characterize them by these conditions, namely the "norm controlled dual limit" (NCDL)-conditions (see \citeLud-Reg). The methods used for the nilpotent Lie groups are different for each. We consider the co-adjoint orbits and for our case, we use the Kirillov theory.

Related

• The C*-algebras of connected real two-step nilpotent Lie groups
• Fourier transforms of C^*-algebras of nilpotent Lie groups
• C*-algebras with norm controlled dual limits and nilpotent Lie groups
• The C*-algebra of SL(2,R)
• Topological aspects of group C^*-algebras