location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword PoincarÃ©-Birkhoff-Witt theorem

 Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2012 (vol 65 pp. 241)

Aguiar, Marcelo; Lauve, Aaron
 Lagrange's Theorem for Hopf Monoids in Species Following Radford's proof of Lagrange's theorem for pointed Hopf algebras, we prove Lagrange's theorem for Hopf monoids in the category of connected species. As a corollary, we obtain necessary conditions for a given subspecies $\mathbf k$ of a Hopf monoid $\mathbf h$ to be a Hopf submonoid: the quotient of any one of the generating series of $\mathbf h$ by the corresponding generating series of $\mathbf k$ must have nonnegative coefficients. Other corollaries include a necessary condition for a sequence of nonnegative integers to be the dimension sequence of a Hopf monoid in the form of certain polynomial inequalities, and of a set-theoretic Hopf monoid in the form of certain linear inequalities. The latter express that the binomial transform of the sequence must be nonnegative. Keywords:Hopf monoids, species, graded Hopf algebras, Lagrange's theorem, generating series, PoincarÃ©-Birkhoff-Witt theorem, Hopf kernel, Lie kernel, primitive element, partition, composition, linear order, cyclic order, derangementCategories:05A15, 05A20, 05E99, 16T05, 16T30, 18D10, 18D35
 top of page | contact us | privacy | site map |