We study the infinitesimal (in the sense of Joni and Rota) bialgebra $H_{RT}$ of planar rooted trees introduced in a previous work
of two of the authors,
whose coproduct is given
by deletion of a vertex. We prove that its dual $H_{RT}^*$ is isomorphic to a free non unitary algebra, and give two free generating sets.
Giving $H_{RT}$ a second product, we make it an infinitesimal bialgebra in the sense of Loday and Ronco,
which allows to explicitly construct a projector onto its space of primitive elements, which freely generates $H_{RT}$.
Wang, X., Foıssy, L., & Gao, X. (2023). The dual of infinitesimal unitary Hopf algebras and planar rooted forests. International Electronic Journal of Algebra, 33(33), 178-204. https://doi.org/10.24330/ieja.1220707
AMA
Wang X, Foıssy L, Gao X. The dual of infinitesimal unitary Hopf algebras and planar rooted forests. IEJA. January 2023;33(33):178-204. doi:10.24330/ieja.1220707
Chicago
Wang, Xiaomeng, Loic Foıssy, and Xing Gao. “The Dual of Infinitesimal Unitary Hopf Algebras and Planar Rooted Forests”. International Electronic Journal of Algebra 33, no. 33 (January 2023): 178-204. https://doi.org/10.24330/ieja.1220707.
EndNote
Wang X, Foıssy L, Gao X (January 1, 2023) The dual of infinitesimal unitary Hopf algebras and planar rooted forests. International Electronic Journal of Algebra 33 33 178–204.
IEEE
X. Wang, L. Foıssy, and X. Gao, “The dual of infinitesimal unitary Hopf algebras and planar rooted forests”, IEJA, vol. 33, no. 33, pp. 178–204, 2023, doi: 10.24330/ieja.1220707.
ISNAD
Wang, Xiaomeng et al. “The Dual of Infinitesimal Unitary Hopf Algebras and Planar Rooted Forests”. International Electronic Journal of Algebra 33/33 (January 2023), 178-204. https://doi.org/10.24330/ieja.1220707.
JAMA
Wang X, Foıssy L, Gao X. The dual of infinitesimal unitary Hopf algebras and planar rooted forests. IEJA. 2023;33:178–204.
MLA
Wang, Xiaomeng et al. “The Dual of Infinitesimal Unitary Hopf Algebras and Planar Rooted Forests”. International Electronic Journal of Algebra, vol. 33, no. 33, 2023, pp. 178-04, doi:10.24330/ieja.1220707.
Vancouver
Wang X, Foıssy L, Gao X. The dual of infinitesimal unitary Hopf algebras and planar rooted forests. IEJA. 2023;33(33):178-204.