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