. O A ] 8 O ct 1 99 8 GROTHENDIECK GROUP INVARIANTS FOR PARTLY SELF - ADJOINT OPERATOR ALGEBRAS

2 2 Ja n 19 99 GROTHENDIECK GROUP INVARIANTS FOR PARTLY SELF - ADJOINT OPERATOR ALGEBRAS

Partially ordered Grothendieck group invariants are introduced for general operator algebras and these are used in the classification of direct systems and direct limits of finite-dimensional complex incidence algebras with common reduced digraph H (systems of H-algebras). In particular the dimension distribution group G(A; C), defined for an operator algebra A and a self-adjoint subalgebra C, ...

m at h . O A ] 3 1 A ug 1 99 8 RELATIVE POSITIONS OF MATROID ALGEBRAS

A classification is given for regular positions D ⊕ D ⊆ D of Jones index 4 where D = alg lim −→ M n k (C) is an even matroid algebra and where the individual sum-mands have index 2. A similar classification is obtained for positions of direct sums of 2-symmetric algebras and, in the odd case, for the positions of sums of 2-symmetric C*-algebras in matroid C*-algebras. The approach relies on an ...

[ m at h . SP ] 9 O ct 1 99 8 SPECTRAL INSTABILITY FOR SOME SCHRÖDINGER OPERATORS

We define the concept of instability index of an isolated eigenvalue of a non-self-adjoint operator, and prove some of its general properties. We also describe a stable procedure for computing this index for Schrödinger operators in one dimension, and apply it to the complex resonances of a typical operator with a dilation analytic potential. AMS subject classification: 34L05, 35P05, 47A75, 49R...

2 3 O ct 1 99 8 PERIODIC CYCLIC HOMOLOGY AS SHEAF COHOMOLOGY

0. Introduction. This paper continues the study of the noncommutative infinitesimal cohomology we introduced in [3]. This is the cohomology of sheaves on a noncommutative version of the commutative infinitesimal site of Grothendieck ([8]). Grothendieck showed that, for a smooth scheme X of characteristic zero, the cohomology of the structure sheaf on the infinitesimal site gives de Rham cohomol...

m at h . Q A ] 2 5 O ct 1 99 8 Spherical 2 - categories and 4 - manifold invariants