On the Wildness of Cambrian Lattices
Copyright policy )On the Wildness of Cambrian Lattices
In this note, we investigate the representation type of the cambrian lattices and some other related lattices. The result is expressed as a very simple trichotomy. When the rank of the underlined Coxeter group is at most 2, the lattices are of finite representation type. When the Coxeter group is a reducible group of type A 3 1 , the lattices are of tame representation type. In all the other cases they are of wild representation type.
representation type, Cluster algebras, Representation type (finite, tame, wild, etc.) of associative algebras, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Representation type, Poset, poset, Cambrian, FOS: Mathematics, Representations of quivers and partially ordered sets, Mathematics - Combinatorics, Combinatorics (math.CO), [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), Cambrian lattice, Mathematics - Representation Theory
representation type, Cluster algebras, Representation type (finite, tame, wild, etc.) of associative algebras, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Representation type, Poset, poset, Cambrian, FOS: Mathematics, Representations of quivers and partially ordered sets, Mathematics - Combinatorics, Combinatorics (math.CO), [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), Cambrian lattice, Mathematics - Representation Theory
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