A Hopf algebra of subword complexes

Abstract

We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra induces a natural non-trivial sub-Hopf algebra on $c$-clusters in the theory of cluster algebras.

Several color figures, 31 pages

References in corpus (2)

• Hopf Algebras and Markov Chains
• Cluster algebras of type D: pseudotriangulations approach

Cited by in corpus (5)

• Hypergraphic polytopes: combinatorial properties and antipode
• Hopf dreams and diagonal harmonics
• Cancelation free formula for the antipode of linearized Hopf monoid
• Markov Chains from Descent Operators on Combinatorial Hopf Algebras
• Combinatorial foundations for geometric realizations of subword complexes of Coxeter groups