Laurent phenomenon algebras
نویسنده
چکیده
We generalize Fomin and Zelevinsky’s cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.
منابع مشابه
The Broken Ptolemy Algebra: a Finite-type Laurent Phenomenon Algebra
Type A, or Ptolemy cluster algebras are a prototypical example of finite type cluster algebras, as introduced by Fomin and Zelevinsky. Their combinatorics is that of triangulations of a polygon. Lam and Pylyavskyy have introduced a generalization of cluster algebras where the exchange polynomials are not necessarily binomial, called Laurent phenomenon algebras. It is an interesting and hard que...
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We develop a new approach to cluster algebras based on the notion of an upper cluster algebra, defined as an intersection of Laurent polynomial rings. Strengthening the Laurent phenomenon established in [6], we show that, under an assumption of “acyclicity”, a cluster algebra coincides with its “upper” counterpart, and is finitely generated; in this case, we also describe its defining ideal, an...
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تاریخ انتشار 2012