Roel Willems
Analogue of the Duistermaat-van der Kallen Theorem for Group Algebras.
Thu, 09/30/2010 - 15:01 — SomNambulAuthors: Wenhua Zhao, Roel Willems
Subjects: Rings and Algebras
AbstractLet $G$ be a group, $R$ an integral domain, and $V_G$ the subspace of the
group algebra $R[G]$ consisting of all the elements of $R[G]$ whose coefficient
of the identity element $1_G$ of $G$ is equal to zero. Motivated by the Mathieu
conjecture [M], the Duistermaat-van der Kallen theorem [DK], and also by recent
studies on the notion of Mathieu subspaces introduced in [Z4] and [Z6], we show
that for finite groups $G$, $V_G$ under certain conditions also forms a Mathieu
subspace of the group algebra $R[G]$.Polynomial automorphisms over finite fields: Mimicking non-tame and tame maps by the Derksen group.
Fri, 12/18/2009 - 16:01 — SomNambulAuthors: Stefan Maubach, Roel Willems
Subjects: Algebraic Geometry
AbstractIf $F$ is a polynomial automorphism over a finite field $\F_q$ in dimension
$n$, then it induces a bijection $\pi_{q^r}(F)$ of $(\F_{q^r})^n$ for every
$r\in \N^*$. We say that $F$ can be `mimicked' by elements of a certain group
of automorphisms $\mathcal{G}$ if there are $g_r\in \mathcal{G}$ such that
$\pi_{q^r}(g_r)=\pi_{q^r}(F)$.
User login
