Multi-parameter local semi-groups of Hermetian operators

Semi-groups of Operators

Shifted Witt Groups of Semi-local Rings

We show that the odd-indexed derived Witt groups of a semilocal ring with trivial involution vanish. We show that this is wrong when the involution is not trivial and we provide examples.

Multi-parameter Cells of Finite Coxeter Groups

Cells of Coxeter groups are certain equivalence classes defined by the Kazhdan-Lusztig type basis of the associated Hecke algebra with a set of parameters. In this paper, we prove that, for finite Coxeter groups, cells arising from a multiparameter Hecke algebra are determined by those arising from a Hecke algebra with parameters which are powers of a single parameter.

Local Analysis for Semi-bounded Groups

An o-minimal expansion M = 〈M, <, +, 0, . . . 〉 of an ordered group is called semi-bounded if it does not expand a real closed field. Possibly, it defines a real closed field with bounded domain I ⊆ M . Let us call a definable set short if it is in definable bijection with a definable subset of some In, and long otherwise. Previous work by Edmundo and Peterzil provided structure theorems for de...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations