The spectral problem and algebras associated with extended Dynkin graphs. I

2006/01/22 by Stanislav Krugljak, Krugljak, Stanislav, Stanislav Popovych +3
Mathematics · #16G20 #16W10 #47L30 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0601533

openalex publication_date 2006/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There is a connection between *-representations of algebras associated with graphs and the problem about the spectrum of a sum of Hermitian operators (spectral problem). For algebras associated with extended Dynkin graphs we give an explicit description of the parameters for which there are *-representations and an algorithm for constructing these representations.

Related

• The spectral problem and *-representations of algebras associated with Dynkin graphs
• The Spectral Problem and Algebras Associated with Extended Dynkin Graphs
• On *-representations of a certain class of algebras related to a graph
• Special characters on star graphs and representations of *-algebras
• Combinatorial spectra of graphs