Special characters on star graphs and representations of $\ast$-algebras

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 $\ast$-algebra have irreducible infinite-dimensional $\ast$-representations, if the graph contains an extended Dynkin graph as a proper subgraph.

10 pages. ver.3: a reference added

References in corpus (4)

• Locally-scalar representations of graphs in the category of Hilbert spaces
• On *-representations of a certain class of algebras related to a graph
• Algebras Generated by Elements with Given Spectrum and Scalar Sum and Kleinian Singularities
• Separating Functions, Spectral Graph Theory and Locally Scalar Representations in Hilbert Spaces