5,759 research outputs found
Homological finiteness properties of monoids, their ideals and maximal subgroups
We consider the general question of how the homological finiteness property
left-FPn holding in a monoid influences, and conversely depends on, the
property holding in the substructures of that monoid. In particular we show
that left-FPn is inherited by the maximal subgroups in a completely simple
minimal ideal, in the case that the minimal ideal has finitely many left
ideals. For completely simple semigroups we prove the converse, and as a
corollary show that a completely simple semigroup is of type left- and
right-FPn if and only if it has finitely many left and right ideals and all of
its maximal subgroups are of type FPn. Also, given an ideal of a monoid, we
show that if the ideal has a two-sided identity element then the containing
monoid is of type left-FPn if and only if the ideal is of type left-FPn.Comment: 25 page
Automorphisms of real Lie algebras of dimension five or less
The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components. For finite-dimensional Lie algebras, there is a well-known algorithm for finding such components, so the theorem considerably simplifies the problem of classifying the automorphism groups. We illustrate this by classifying the automorphisms of all indecomposable real Lie algebras of dimension five or less. Our results are presented very concisely, in tabular form
Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids
This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen & Qui and Güzel Karpuz; we then construct biautomatic structures. For hypoplactic monoids, we construct finite complete rewriting systems and biautomatic structures. For sylvester monoids, which are not finitely presented, we prove that the standard presentation is an infinite complete rewriting system, and construct biautomatic structures. Consequently, the monoid algebras corresponding to monoids of these classes are automaton algebras in the sense of Ufnarovskij
A Svarc-Milnor lemma for monoids acting by isometric embeddings
We continue our programme of extending key techniques from geometric group
theory to semigroup theory, by studying monoids acting by isometric embeddings
on spaces equipped with asymmetric, partially-defined distance functions. The
canonical example of such an action is a cancellative monoid acting by
translation on its Cayley graph. Our main result is an extension of the
Svarc-Milnor Lemma to this setting.Comment: 11 page
UTSim2 validation
The Center for NDE (CNDE) at Iowa State University has a long history of developing physics models for NDE and packaging these models into simulation tools which make the modeling capabilities accessible to CNDEs industrial sponsors. Recent work at CNDE has led to the development of a new ultrasonic simulation package, UTSim2, which aims to continue this tradition of supporting industrial application of CNDE models. In order to meet this goal, UTSim2 has been designed as an extensible software package which can support previously-developed physics models as well as future models yet to be developed. Initial work has focused on the implementation of a Gauss-Hermite beam model, a paraxial approximation, which is implemented as part of the Thompson-Gray measurement model. This paper will present recent validation results and include comparisons against both previously-validated model output and newly-performed experiments
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