The Wave Equation in the Context of Reduced Groups C^*-Algebras

2025/05/28 by Huang Fan, Huang, Fan
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.22930

openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the identification C(\mathbbT)≅ C_r^*(ℤ) and the wave equation on the circle, we explore the wave equation in the context of reduced group C^*-algebras C_r^*(G) for countably infinite, possibly non-abelian groups G. Using a one-parameter group of *-automorphisms whose infinitesimal generator paves the way to an analogue of the Laplacian, we establish the existence and uniqueness of solutions to the wave equation within this framework.

Citations

• Heat properties for groups
• One-parameter semigroups for linear evolution equations

Related

• The C^*-algebra of the group N₇.
• C^*-algebras associated with the ax+b-semigroup over \mathbb N
• Crystallization of C*-algebras
• Traces of C^*-algebras of connected solvable groups
• Structural properties of reduced C^*-algebras associated with higher-rank lattices