1,405 research outputs found
SgpDec : Cascade (de)compositions of finite transformation semigroups and permutation groups
We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products.Final Accepted Versio
Green's relations on the deformed transformation semigroups
Green's relations on the deformed finite inverse symmetric semigroup
and the deformed finite symmetric semigroup
are described.Comment: 11 page
Invariant means on Boolean inverse monoids
The classical theory of invariant means, which plays an important role in the
theory of paradoxical decompositions, is based upon what are usually termed
`pseudogroups'. Such pseudogroups are in fact concrete examples of the Boolean
inverse monoids which give rise to etale topological groupoids under
non-commutative Stone duality. We accordingly initiate the theory of invariant
means on arbitrary Boolean inverse monoids. Our main theorem is a
characterization of when a Boolean inverse monoid admits an invariant mean.
This generalizes the classical Tarski alternative proved, for example, by de la
Harpe and Skandalis, but using different methods
Regular obstructed categories and TQFT
A proposal of the concept of -regular obstructed categories is given. The
corresponding regularity conditions for mappings, morphisms and related
structures in categories are considered. An n-regular TQFT is introduced. It is
shown the connection of time reversibility with the regularity.Comment: 22 pages in Latex. To be published in J. Math. Phy
Spectral asymptotics of periodic elliptic operators
We demonstrate that the structure of complex second-order strongly elliptic
operators on with coefficients invariant under translation by
can be analyzed through decomposition in terms of versions ,
, of with -periodic boundary conditions acting on
where . If the semigroup generated by
has a H\"older continuous integral kernel satisfying Gaussian bounds then the
semigroups generated by the have kernels with similar properties
and extends to a function on which is
analytic with respect to the trace norm. The sequence of semigroups
obtained by rescaling the coefficients of by converges in
trace norm to the semigroup generated by the homogenization
of . These convergence properties allow asymptotic analysis of
the spectrum of .Comment: 27 pages, LaTeX article styl
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