Involutorial Transformations

Tori Invariant under an Involutorial Automorphism I

Let G be a connected reductive linear algebraic group defined over an field k of characteristic not 2, θ ∈ Aut(G) an involutional k-automorphism of G and K = Gθ = {g ∈ G | θ(g) = g} the set of fixed points of θ. Denote the set of k-rational points of G by Gk. In this paper we shall classify the K-conjugacy classes of θ-stable maximal tori of G. This is shown to be independent of the characteris...

Tori Invariant under an Involutorial Automorphism Ii

The geometry of the orbits of a minimal parabolic k-subgroup acting on a symmetric k-variety is essential in several area’s, but its main importance is in the study of the representations associated with these symmetric k-varieties (see for example [6], [5], [20] and [31]). Up to an action of the restricted Weyl group of G, these orbits can be characterized by the Hk-conjugacy classes of maxima...

On p-semilinear transformations

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

A Series of Involutorial Cremona Space Transformations D E F I N E D by a Pencil of Ruled Cubic Surfaces* by Amos Black

Transformations Debugging Transformations

Practical model transformation (MT) frameworks are usually composed of multiple execution contexts, building an overall workflow by abstracting different aspects of execution. This heterogeneity brings additional challenges to debugging, which must address a combination of quite different graphical and textual formalisms. In this work we describe a layered approach to debugging, mapping familia...