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LAGRANGE’S THEOREM FOR HOPF MONOIDS IN SPECIES
Hopf monoids species graded Hopf algebras
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2015/8/14
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
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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...
HOPF MONOIDS IN THE CATEGORY OF SPECIES
Species Hopf monoid Lie monoid antipode Hadamard product
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2015/8/14
A Hopf monoid (in Joyal’s category of species) is an algebraic
structure akin to that of a Hopf algebra. We provide a self-contained introduction
to the theory of Hopf monoids in the category of spe...