A Hopf Operad of Forests of Binary Trees and Related Finite-Dimensional Algebras
Frédéric Chapoton
DOI: 10.1023/B:JACO.0000048517.19053.ff
Abstract
The structure of a Hopf operad is defined on the vector spaces spanned by forests of leaf-labeled, rooted, binary trees. An explicit formula for the coproduct and its dual product is given, using a poset on forests.
Pages: 311–330
Keywords: Hopf operad; binary tree; poset
Full Text: PDF
References
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1998. Translated from the 1994 French original by Margaret Readdy, With a foreword by Gian-Carlo Rota.
3. F.R. Cohen, “The homology of Cn+1-spaces, n \geq 0,” in The Homology of Iterated Loop Spaces, Vol. 533 of Lecture Notes, Springer-Verlag (1976) pp. 207-351.
4. V. Ginzburg and M. Kapranov, “Koszul duality for operads,” Duke Math. J. 76(1) (1994), 203-272.
5. E. Grosswald, Bessel Polynomials, Springer, Berlin (1978).
6. H.L. Krall and O. Frink, “A new class of orthogonal polynomials: The Bessel polynomials,” Trans. Amer. Math. Soc. 65 (1949), 100-115.
7. M. Markl, “Distributive laws and Koszulness,” Ann. Inst. Fourier (Grenoble) 46(2) (1996), 307-323.
8. M. Markl, S. Shnider, and J. Stasheff, Operads in Algebra, Topology and Physics, American Mathematical Society, Providence, RI (2002).
9. J.P. May, “Definitions: Operads, algebras and modules,” in Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), Providence, RI, Amer. Math. Soc. (1997), pp. 1-7.
10. A.A. Voronov, “Homotopy Gerstenhaber algebras,” in Conférence Moshé Flato 1999, Kluwer Acad. Publ., Dordrecht, Vol. II (Dijon) (2000), pp. 307-331.