Decomposition of Exact pfd Persistence Bimodules

Comparison of PFD calculation

Safety systems are be used in a wide range of technical application. Beside the availability of such systems the safety aspects, e. g. PFD and PFH figures, must be observed. Especially the calculation of these figures requires the use of standards. Worldwide are standards available for this calculation. The newest standard is IEC 61508. This standard is worldwide accepted. Another standard, whi...

Endomorphism rings of bimodules

Lecture 11: Soergel Bimodules

In this lecture we continue to study the category O0 and explain some ideas towards the proof of the Kazhdan-Lusztig conjecture. We start by introducing projective functors Pi : O0 → O0 that act by w 7→ w(1 + si) on K0(O0). Using these functors we produce a projective generator of O0. In Section 2 we explain some of the work of Soergel that ultimately was used by Elias and Williamson to give a ...

Separable bimodules and approximation

Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant finiteness of the subcategory of (finitely generated) left modules with finite projective dimension, finitistic dimension, finite representation type, Ausland...

Bimodules and Abelian Surfaces

Introduction In a manuscript on mod representations attached to modular forms [26], the author introduced an exact sequence relating the mod p reduction of certain Shimura curves and the mod q reduction of corresponding classical modular curves. Here p and q are distinct primes. More precisely, fix a maximal order O in a quaternion algebra of discriminant pq over Q. Let M be a positive integer ...