‎let $r$ be a $*$-prime ring with center‎ ‎$z(r)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $r$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $r$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎suppose that $u$ is an ideal of $r$ such that $u^*=u$‎, ‎and $c_{sigma,tau}={cin‎ ‎r~|~csigma(x)=tau(x)c~mbox{for~all}~xin r}.$ in the present paper‎, ‎it is shown that...

Theorem 1.1. There exists a holomorphic map σ of C of the form ξ → λξ + O(2), η → λη + O(2), with λ not a root of unity and |λ| = 1, such that σ is reversible by an antiholomorphic involution and by a formal holomorphic involution, and is however not reversible by any C-smooth involution of which the linear part is holomorphic. In particular, the σ is not reversible by any holomorphic involution.

1. Preliminaries. We are concerned with involutions without fixed points, together with equivariant maps connecting such involutions. An involution T is a homeomorphism of period 2 of a Hausdorff space X onto itself; that is, T(x) = x for all x £ X . There is associated with an involution T on X the orbit space X/T, obtained by identifying x with T(x) for all x G Z . Denote by v\ X—+X/T the dec...

M. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kähler manifold preserved by the complexification of the Hamiltonian group action. V. Guillemin and R. Sjamaar generalized this result to irreducible subvarieties preserved only by a Borel subgroup. In another direction, L. O’Shea and R. Sjamaar proved a convexity result for the moment...

Let R be a ring with involution containing nontrivial symmetric idempotent element e and δ: → generalized ∗-reverse derivable map. In this paper, our aim is to show that under some suitable restrictions imposed on every map of additive.

The six permutations of three elements #i, x 2 , x 3 considered as projective coordinates in a plane determine an involution of sextuples of points which may be mapped on a rational surface, f I shall show that in case of the involution thus defined the map is a quadric whose relation with the plane, established with sufficient details, will lead to some interesting geometric applications. The ...

In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general type S with pg = q = 1 having an involution i such that S/i is a non-ruled surface and such that the bicanonical map of S is not composed with i. A complete list of possibilities is given and several new examples are constructed, as bidouble covers of surf...

We determine the possible cohomology algebra of orbit space of any free involution on a mod-2 cohomology lens space X using the Leray spectral sequence associated to the Borel fibration X →֒ XZ2 −→ BZ2 . As an application we show that if X is a mod-2 cohomology lens space of dimension 2m − 1 where 4 ∤ m, then there does not exist any Z2-equivariant map S n → X for n ≥ 2, where S is equipped with...

We study the minimal complex surfaces of general type with pg = 0 and K 2 = 7 or 8 whose bicanonical map is not birational. We show that if S is such a surface, then the bicanonical map has degree 2 (see [MP1]) and there is a fibration f : S → P such that: i) the general fibre F of f is a genus 3 hyperelliptic curve; ii) the involution induced by the bicanonical map of S restricts to the hypere...

Grafting a measured lamination on a hyperbolic surface defines a self-map of Teichmüller space, which is a homeomorphism by a result of Scannell and Wolf. In this paper we study the large-scale behavior of pruning, which is the inverse of grafting. Specifically, for each conformal structure X ∈ T (S), pruning X gives a map ML (S) → T (S). We show that this map extends to the Thurston compactifi...