For any complex valued functions over topological space F there exists a relation in von Neumann algebras of *-graded that is bounded on compact Hausdorff where for category- I, II, III commutative form 〖AW〗^* such to satisfy monotone complete C^* algebra suffice an isomorphic factor f the same tamed as W^* having generators η generic group η(G) 2-groups G_+ and G_- former being additive intege...

We show how to construct a graded locally compact Hausdorff \'etale groupoid from C*-algebra carrying coaction of discrete group, together with suitable abelian subalgebra. call this the extended Weyl groupoid. When is trivial and subalgebra Cartan, our agrees Renault's prove that if G second-countable grading interior trivially isotropy torsion free, then its reduced isomorphic as G. In partic...

If D is a tame central division algebra over a Henselian valued field F , then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF . After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map ...

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...