TL;DR
This paper explores the Koszul duality of quadri-algebras, proves their koszularity, and introduces quadri-bialgebras with applications to certain Hopf algebras, confirming a conjecture by Aguiar and Loday.
Contribution
It provides the Koszul dual of the operad Quad, proves its koszularity, and introduces quadri-bialgebras with relevant applications.
Findings
Confirmed the conjecture by Aguiar and Loday.
Derived the formal series of Quad and its dual.
Introduced the notion of quadri-bialgebra with applications.
Abstract
WWe describe the Koszul dual of the operad Quad of quadri-algebras, show the koszularity of Quad and give the formal series of Quad and its dual, which proves a conjecture due to Aguiar and Loday. A notion of quadri-bialgebra is also introduced, with applications to the Hopf algebras FQSym and WQSym.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras