The spectral problem and *-representations of algebras associated with Dynkin graphs

2004/07/24 by Stanislav Krugljak, Krugljak, Stanislav, Stanislav Popovych +4
Mathematics · #16G20 #16W10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16G20 #msc:16W10

paper · pdf · doi:10.48550/arxiv.math/0407418

16 pages

openalex publication_date 2004/07/24 · arxiv created 2004/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the connection between *-representations of algebras associated with graphs, locally-scalar graph representations and the problem about the spectrum of a sum of two Hermitian operators. For algebras associated with Dynkin graphs we give an explicit description of the parameters for which there are irreducible representations and an algorithm for contructing these representations.

Related

• The spectral problem and algebras associated with extended Dynkin graphs. I
• On *-representations of a certain class of algebras related to a graph
• The Spectral Problem and Algebras Associated with Extended Dynkin Graphs
• Locally-scalar representations of graphs in the category of Hilbert spaces
• Special characters on star graphs and representations of *-algebras