Confluence Theory for Graphs

Details Confluence Theory for Graphs Confluence Theory for Graphs

2006-09-29

arxiv.org/abs/math/0609832v1

Mathematics

Quantum Algebra

34 pages, 218 figures

Scientific paper

We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of graphs (via Kuperberg's spiders) in an arbitrary surface. As a further consequence of this result, we find canonical bases of SU_3-skein modules of cylinders over orientable surfaces.

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