Lagrange's Theorem for Hopf Monoids in Species

Autor:	Aguiar, Marcelo, Lauve, Aaron
Rok vydání:	2011
Předmět:	Mathematics - Combinatorics Mathematics - Category Theory Mathematics - Quantum Algebra 05A15 05A20 05E99 16T05 16T30 18D10 18D35
Zdroj:	Can. J. Math.-J. Can. Math. 65 (2013) 241-265
Druh dokumentu:	Working Paper
DOI:	10.4153/CJM-2011-098-9
Popis:	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 K of a Hopf monoid H to be a Hopf submonoid: the quotient of any one of the generating series of H by the corresponding generating series of K must have nonnegative coefficients. Other corollaries include a necessary condition for a sequence of nonnegative integers to be the sequence of dimensions 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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1105.5572 Zobrazit plný text záznamu View this record from Arxiv