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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 cond...
HOPF MONOIDS FROM CLASS FUNCTIONS ON UNITRIANGULAR MATRICES
Unitriangular matrix class function superclass function
2015/8/14
We build, from the collection of all groups of unitriangular matrices, Hopf
monoids in Joyal’s category of species. Such structure is carried by the collection of
class function spaces on those grou...
A slight modification of the definition of the Thompson-Higman groups Gk,1 and Fk,1 leads to
inverse monoids that map onto Gk,1 (respectively Fk,1), and that have interesting properties: they are fin...