On *-representations of a certain class of algebras related to a graph

2005/06/24 by Vasyl Ostrovskyi, Ostrovskyi, Vasyl
Mathematics · #16G20 #47A62 #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.FA #math.RA #math.RT #msc:16G20 #msc:47A62

paper · pdf · doi:10.48550/arxiv.math/0506505

7 pages. Submitted to MFAT

arxiv created 2005/06/24 · arxiv updated 2009/12/01

Abstract

We study families of self-adjoint operators with given spectra whose sum is a scalar operator. Such families are *-representations of certain algebras which can be described in terms of graphs and positive functions on them. The main result is that in the cases where the graph is one of the extended Dynkin graphs D₄, E₆, E₇ or E₈, all irreducible *-representations of the corresponding algebra are finite-dimensional. To prove this fact, we introduce the notion of invariant functional on a graph and give their description.

Related

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