Dans cette note, on présente l’énoncé et les principales idées de la démonstration d’un théorème de convexité réel pour les applications moment à valeurs dans un groupe de Lie. Ce résultat est un analogue quasi-hamiltonien du théorème de O’Shea et Sjamaar dans le cadre hamiltonien usuel. On démontre que l’image par l’application moment du lieu des points fixes d’une involution renversant la 2-f...

Coxeter-Petrie complexes naturally arise as thin diagram geometries whose rankthree residues contain all of the dual forms of a regular algebraic mapM. Corresponding to an algebraic map is its classical dual, which is obtained simply by interchanging the vertices and faces, as well as its Petrie dual, which comes about by replacing the faces by the so-called Petrie polygons. G. A. Jones and J. ...

Let Λ be a ring endowed with an involution a 7→ ã. We say that two units a and b of Λ fixed under the involution are congruent if there exists an element u ∈ Λ× such that a = ubũ. We denote by H(Λ) the set of congruence classes. In this paper we consider the case where Λ is an order with involution in a semisimple algebraA over a local field and study the question whether the natural map H(Λ)→ ...

This paper describes how to compute equations of plane models of minimal Du Val double planes of general type with pg = q = 1 and K = 2, . . . , 8. A double plane with K = 8 having bicanonical map not composed with the associated involution is also constructed. The computations are done using the algebra system Magma. 2000 Mathematics Classification: 14J29, 14Q05.

A formula is given for the discriminant of the tensor product of the canonical involution on a quaternion algebra and an orthogonal involution on a central simple algebra of degree divisible by 4. As an application, an alternative proof of Shapiro’s “Pfister Factor Conjecture” is given for tensor products of at most five quaternion algebras. Throughout this paper, the characteristic of the base...

This paper describes how to compute equations of plane models of minimal Du Val double planes of general type with pg = q = 1 and K2 = 2, . . . , 8. A double plane with K2 = 8 having bicanonical map not composed with the associated involution is also constructed. The computations are done using the algebra system Magma.

The Mullineux involution is a relevant map that appears in the study of modular representations symmetric group and alternating group. fixed points this are certain partitions particular interest. It known cardinality set these self-Mullineux equal to distinguished subset self-conjugate partitions. In work, we give an explicit bijection between two families terms symbol.

Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an involution that is also in the group of polynomial automorphisms. This form is a composition of a sequence of generalized Hénon maps together with two simple involu...

‎Let $R$ be a ring with involution $*$‎. ‎An additive mapping $T:Rto R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,yin R$‎. ‎The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.