BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yannic Vargas (University of Potsdam) DTSTART:20211015T130000Z DTEND:20211015T140000Z DTSTAMP:20260423T021649Z UID:ACPMS/14 DESCRIPTION:Title: M onomial bases for combinatorial Hopf algebras\nby Yannic Vargas (Unive rsity of Potsdam) as part of Algebraic and Combinatorial Perspectives in t he Mathematical Sciences\n\n\nAbstract\nThe algebraic structure of a Hopf algebra can often be understood in terms of a poset on the underlying fami ly of combinatorial objects indexing a basis. For example\, the Hopf algeb ra of quasisymmetric functions is generated (as a vector space) by composi tions and admits a fundamental (F) basis and a monomial (M) basis\, relate d by the refinement poset on compositions. Analogous bases can be consider ed for other Hopf algebras\, with similar properties to the F basis\, e.g. a product described by some notion of shuffle\, and a coproduct following some notion of deconcatenation. We give axioms for how these generalised shuffles and deconcatentations should interact with the underlying poset s o that a monomial-like basis can be analogously constructed\, generalising the approach of Aguiar and Sottile. We also find explicit positive formul as for the multiplication on monomial basis and a cancellation-free and gr ouping-free formula for the antipode of monomial elements. We apply these results on classical and new Hopf algebras\, related by tree-like structur es.\nThis is based on "Hopf algebras of parking functions and decorated pl anar trees"\, a joint work with Nantel Bergeron\, Rafael Gonzalez D'Leon\, Amy Pang and Shu Xiao Li.\n LOCATION:https://researchseminars.org/talk/ACPMS/14/ END:VEVENT END:VCALENDAR