Christoffel Words and Markoff Triples: An Algebraic Approach

Details Christoffel Words and Markoff Triples: An Algebraic Approach Christoffel Words and Markoff Triples: An Algebraic Approach

2011-04-10

arxiv.org/abs/1104.1799v3

Mathematics

Representation Theory

18 pages; v2: corrected typos, revised two proofs in section 4; v3: final version to appear in Communications in Algebra

Scientific paper

We introduce a family of modules, called Markoff modules, generated by a cluster-mutation-like iterative process. We show that these modules are combinatorially similar to Christoffel words. Furthermore, we construct a bijective map between the set of Markoff module triples and the set of proper Markoff triples. This allows us to interpret the uniqueness conjecture for Markoff numbers within an algebraic framework.

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