Complex structures on real vector lattices

An equivalence functor between local vector lattices and vector lattices

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

Cyclotomic structures on root lattices

The centralizer C(w) of an element w in a Weyl group W plays an important role in the structure and representation theory of split reductive groups G over finite and p-adic fields k, where W is the absolute Weyl group of G. If k is finite, this is well-known: the element w determines a maximal ktorus Tw ⊂ G and C(w) may be identified with the k-rational points in the Weyl group W (Tw, G) of Tw ...

8-th International Workshop on Complex structures and vector fields

On finite elements in vector lattices and Banach lattices

In Archimedean vector lattices we show that each element of the band generated by a finite element is also finite. In vector lattices with the (PPP) and in Banach lattices we obtain some characterizations of finite elements by using the generalized order units for principal bands. In the case of Banach lattices with order continuous norm the ideal of all finite elements coincides with the linea...

Poisson Structures on Complex Flag Manifolds Associated with Real Forms

For a complex semisimple Lie group G and a real form G0 we define a Poisson structure on the variety of Borel subgroups of G with the property that all G0-orbits in X as well as all Bruhat cells (for a suitable choice of a Borel subgroup of G) are Poisson submanifolds. In particular, we show that every non-empty intersection of a G0-orbit and a Bruhat cell is a regular Poisson manifold, and we ...