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

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

2005-09-12

arxiv.org/abs/math/0509240v3

Mathematics

Rings and Algebras

10 pages. ver.3: a reference added

Scientific paper

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.

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