arXiv subjects
Publications and source records attributed to George Nadareishvili.
Standard analyses of expected runtimes for randomized algorithms typically bypass the explicit construction of an underlying probability space. In this paper, we provide a formal, yet intuitive tree-based definition of the probability space for the execution paths of such algorithms. Using this model, we derive the recurrence equation for the expected runtime.
We prove a Universal Coefficient Theorem for objects in the bootstrap class in the equivariant Kasparov category for a finite cyclic group of square-free order.
The equivariant bootstrap class in the Kasparov category of actions of a finite group G consists of those actions that are equivalent to one on a Type I C*-algebra. Using a result by Arano and Kubota, we show that this bootstrap class is already generated by the continuous functions on G/H for all cyclic subgroups H of G. Then we prove a Universal Coefficient Theorem for the localisation of this bootstrap class at the group order |G|. This allows us to classify certain G-actions on stable Kirchberg algebras up to cocycle conjugacy.
This survey article on relative homological algebra in bivariant K-thoery is mainly intended for readers with a background knowledge in triangulated categories. We briefly recall the general theory of relative homological algebra in triangulated categories and latter specialize it to the non-equivariant and the equivariant bivariant K-thoery, where the actions on C*-algebras is by a finite cyclic group. We conclude by the explicit computation of the universal abelian invariant for separable C*-algebras with the action of $\mathbb{Z}/4$ by automorphisms.
We use the abelian approximation for the bootstrap category of filtered C*-algebras to define a sensible notion of support for its objects. As a consequence, we provide a full classification of localizing subcategories in terms of a product of lattices of noncrossing partitions of a regular $(n+1)$-gon, where $n$ is the number of ideals in the filtration.