We classify the split simple affine algebraic groups G of types A and C over a field with the property that the Chow group of the quotient variety E/P is torsion-free, where P ⊂ G is a special parabolic subgroup (e.g., a Borel subgroup) and E is a generic G-torsor (over a field extension of the base field). Examples of G include the adjoint groups of type A. Examples of E/P include the Severi-B...

In this article we describe the G×G-equivariant K-ring of X, where X is a regular compactification of a connected complex reductive algebraic group G. Furthermore, in the case when G is a semisimple group of adjoint type, and X its wonderful compactification, we describe its ordinary K-ring K(X). More precisely, we prove that K(X) is a free module over K(G/B) of rank the cardinality of the Weyl...

According to J. Feldman and C. Moore’s wellknown theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e., a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave a C∗-algebraic analogue of this theore...

We study the data transformation capabilities associated with schemas that are presented by labeled directed multi-graphs and path equivalence constraints. Unlike most approaches which treat graph-based schemas as abbreviations for relational schemas, we treat graph-based schemas as categories. A morphism M between schemas S and T , which can be generated from a visual mapping between graphs, i...

Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of some anisotropic projective G-homogeneous varieties in terms of motives of simpler G-homogeneous varieties, namely, those that correspond to maximal parabolic subgroups of G. We decompose the motive of a generalized Severi-Brauer variety SB2(A), where A is a division algebra of d...

In the previous two parts of this series of papers, we introduced and studied a large class of analytic difference operators admitting reflectionless eigenfunctions, focusing on algebraic and function-theoretic features in the first part, and on connections with solitons in the second one. In this third part we study our difference operators from a quantum mechanical viewpoint. We show in parti...

We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of s...

In this paper, we describe the category of bi-equivariant vector bundles on a bi-equivariant smooth (partial) compactification of a reductive algebraic group with normal crossing boundary divisors. Our result is a generalization of the description of the category of equivariant vector bundles on toric varieties established by A. As an application, we prove splitting of equivariant vector bundle...

We are interested in the simulation and optimization of gas transport in networks. Those networks consist of pipes and various other components like compressor stations and valves. The gas flow through the pipes can be modelled by different equations based on the Euler equations. For the other components, purely algebraic equations are used. Depending on the data, different models for the gas f...

A quandle is an algebraic system with a binary operation satisfying three axioms modelled on the Reidemeister moves of planar diagrams links in 3-space. The paper establishes new relationship between cohomology, extensions and automorphisms quandles. We derive four term exact sequence relating 1-cocycles, second cohomology certain group abelian extension non-abelian counterpart this involving d...