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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...
HOPF MONOIDS IN THE CATEGORY OF SPECIES
Species Hopf monoid Lie monoid antipode Hadamard product
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...
Inverse semigroups determined by their partial automorphism monoids
Inverse semigroups partial automorphism monoids Rings and Algebras
2011/9/20
Abstract: The partial automorphism monoid of an inverse semigroup is an inverse monoid consisting of all isomorphisms between its inverse subsemigroups. We prove that a tightly connected fundamental i...
Universality of the lattice of transformation monoids
algebraic lattice embedding transformation monoid
2011/9/15
Abstract: The set of all transformation monoids on a fixed set of infinite cardinality lambda, equipped with the order of inclusion, forms an algebraic lattice Mon(lambda) with 2^lambda compact elemen...
Knuth-Bendix algorithm and the conjugacy problems in monoids
Knuth-Bendix algorithm conjugacy problems monoids
2011/2/21
We present an algorithmic approach to the conjugacy problems in monoids, using rewriting systems. We extend the classical theory of rewriting developed by Knuth and Bendix to a rewriting that takes in...
On properties not inherited by monoids from their Schutzenberger groups
Complete rewriting systems Finitely presented groups and monoids Finiteness conditions
2011/1/20
We give an example of a monoid with finitely many left and right ideals, all of whose Sch¨utzenberger groups are presentable by finite complete rewriting systems, and so each have finite derivation ty...
Let A be a not necessarily commutative monoid with zero such that projective A-acts are free. This paper shows that the algebraic K-groups of A can be defined using the +-construction and the Q-constr...
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...
The Bergman property for endomorphism monoids of some Fraïssé limits
Bergman property for endomorphism monoids Fraï ssé limits
2010/12/3
Based on an idea of Y. P´eresse and some results ofMaltcev, Mitchell and Ruˇskuc,we present sufficient conditions under which the endomorphism monoid of an ultrahomogeneous first-order structure...
Primitive orthogonal idempotents for R-trivial monoids
orthogonal idempotents R-trivial monoids
2010/12/13
We show that the notions of R-trivial monoid and weakly ordered monoid are equivalent. We use this fact to construct a complete system of orthogonal idempotents for all R-trivial monoids.
On monoids of almost identity injective partial selfmaps
Topological semigroup semitopological semigroup topological inverse semigroup
2010/12/1
In the paper we study the semigroup I1 of almost identity injective partial selfmaps of the
set of cardinality .
Growth partition functions for cancellative infinite monoids
Growth partition functions cancellative infinite monoids
2010/12/15
We introduce the growth partition function Z,G(t)associated with any cancellative infinite monoid with a finite generator system G. It is a power series in t whose coefficients
l...
A universality result for endomorphism monoids of some ultrahomogeneous structures
endomorphism monoid Fra¨ı ss´ e limit pushout
2010/12/7
We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra¨ıss´e limit) embeds all countable semigr...
We introduce stochastic monoids and stochastic congruences and we investigate their basic properties.