Special characters on star graphs and representations of $*$-algebras

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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.
10 pages. ver.3: a reference added

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Rings and Algebras, Functional Analysis, Representation Theory, 16G20; 47A62

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http://salesiana.dossiersoluciones.com/handle/123456789/102254

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509240
 http://arxiv.org/abs/math/0509240

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arXiv