Examples of Com-PreLie Hopf algebras
Lo\"ic Foissy (LMPA)
TL;DR
This paper presents various examples and classifications of Com-PreLie bialgebras, including constructions on shuffle algebras, polynomial algebras, and the classification of connected cocommutative cases.
Contribution
It introduces new families of Com-PreLie bialgebras on shuffle algebras and classifies all connected cocommutative Com-PreLie bialgebras.
Findings
Defined three families of Com-PreLie bialgebras on shuffle algebras.
Classified all graded preLie products on K[X].
Provided a complete classification of connected cocommutative Com-PreLie bialgebras.
Abstract
We gives examples of Com-PreLie bialgebras, that is to say bialgebras with a preLie product satisfying certain compatibilities. Three families are defined on shuffle algebras: one associated to linear endomorphisms, one associated to linear form, one associated to preLie algebras. We also give all graded preLie product on K[X], making this bialgebra a Com-PreLie bialgebra, and classify all connected cocommutative Com-PreLie bialgebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Operator Algebra Research