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David Riley

Publications and source records attributed to David Riley.

4 recordsLinked to original sources
arXiv2025

Presenting the Zassenhaus Lie algebra by the Magnus Lie algebra

It is shown that the Zassenhaus restricted $\mathbb F_p$-Lie algebra of a (pro-p) group G can be presented by the Magnus Lie algebra of G. For the class of (pro-p) groups for which the terms of the lower central series are torsion-free, the Zassenhaus restricted $\mathbb F_p$-Lie algebra can be explicitly computed from the Magnus Lie algebra. These results apply to orientable surface groups, right-angled Artin groups, pure braid groups, fundamental groups of supersolvable hyperplane arrangements and fundamental groups of strictly supersolvable toric arrangements.

math.GR↗
arXiv2025

Roadmap for warm dense matter physics

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the warm dense matter physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations \& experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments and contemporary challenges that are faced by theoretical methods, and experimental techniques needed to create and diagnose warm dense matter. A large part of this roadmap is dedicated to specific warm dense matter systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

physics.plasm-ph↗
arXiv2018

On polynomials that are not quite an identity on an associative algebra

Let $f$ be a polynomial in the free algebra over a field $K$, and let $A$ be a $K$-algebra. We denote by $\S_A(f)$, $\A_A(f)$ and $\I_A(f)$, respectively, the `verbal' subspace, subalgebra, and ideal, in $A$, generated by the set of all $f$-values in $A$. We begin by studying the following problem: if $\S_A(f)$ is finite-dimensional, is it true that $\A_A(f)$ and $\I_A(f)$ are also finite-dimensional? We then consider the dual to this problem for `marginal' subspaces that are finite-codimensional in $A$. If $f$ is multilinear, the marginal subspace, $\widehat{\S}_A(f)$, of $f$ in $A$ is the set of all elements $z$ in $A$ such that $f$ evaluates to 0 whenever any of the indeterminates in $f$ is evaluated to $z$. We conclude by discussing the relationship between the finite-dimensionality of $\S_A(f)$ and the finite-codimensionality of $\widehat{\S}_A(f)$.

math.RA↗