Special characters on star graphs and representations of *-algebras

2005/09/12 by Vasyl Ostrovskyi, Ostrovskyi, Vasyl
Mathematics · #16G20 #47A62 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0509240

openalex publication_date 2005/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a star-shaped graph, we introduce special characters and study their properties. We decompose special characters into odd and even parts and study their evolution under reflections. We apply the obtained formulas to prove that the corresponding *-algebra have irreducible infinite-dimensional *-representations, if the graph contains an extended Dynkin graph as a proper subgraph.

Citations

• Algebras Generated by Elements with Given Spectrum and Scalar Sum and Kleinian Singularities

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 *-representations of algebras associated with Dynkin graphs
• A conjecture concerning *-algebras that unifies some matrix decompositions
• Exceptional Periodicity and Magic Star Algebras. II : Gradings and\n HT-Algebras