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Noncommutative cluster mutations. (Russian. English summary) Zbl 1267.16012
Summary: Non-commutative cluster mutations are defined and studied. For a particular mutation matrix it is proved that the iteration of cluster mutation is assigned by non-commutative Laurent polynomials, and this gives an independent proof of the Laurent phenomenon in the commutative case.

MSC:
16G20 Representations of quivers and partially ordered sets
13F60 Cluster algebras
05E18 Group actions on combinatorial structures
16S38 Rings arising from noncommutative algebraic geometry
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
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