1. CMB Online first
|Octonion Algebras over Rings are not Determined by their Norms|
Answering a question of H. Petersson, we provide a class of examples of pair of octonion algebras over a ring having isometric norms.
Keywords:octonion algebras, torsors, descent
2. CMB 2007 (vol 50 pp. 535)
|Generalized Descent Algebras |
If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-$\ZM$-module $\DC_A(W)$ of the group algebra $\ZM W$. We discuss cases where this submodule is a subalgebra. This family of subalgebras includes strictly the Solomon descent algebra, the group algebra and, if $W$ is of type $B$, the Mantaci--Reutenauer algebra.
Keywords:Coxeter group, Solomon descent algebra, descent set