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Abstract Picantin's iterated crossed product representation of Garside monoids is extended and reproved for a wide class of not necessarily noetherian partially ordered groups with a right invariant lattice structure.… Click to show full abstract
Abstract Picantin's iterated crossed product representation of Garside monoids is extended and reproved for a wide class of not necessarily noetherian partially ordered groups with a right invariant lattice structure. It is shown that the tree-like structure of such an iterated crossed product is equivalent to a partial cycle set, closely related to a class of set-theoretic solutions of the quantum Yang–Baxter equation. The decomposition of finite square-free solutions is related to the crossed product representation of the corresponding structure group.
Journal Title: Journal of Algebra
Year Published: 2017
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