We show how to recover a discrete twist over an ample Hausdorff groupoid from pair consisting of algebra and what we call quasi-Cartan subalgebra. identify precisely which twists arise in this way (namely, those that satisfy the local bisection hypothesis), prove assignment twisted Steinberg algebras such our construction are mutually inverse. algebraic pairs correspond effective groupoids prin...

Tits has defined Kac–Moody and Steinberg groups over commutative rings, providing infinite dimensional analogues of the Chevalley–Demazure group schemes. Here we establish simple explicit presentations for all Steinberg and Kac–Moody groups whose Dynkin diagrams are hyperbolic and simply laced. Our presentations are analogues of the Curtis–Tits presentation of the finite groups of Lie type. Whe...

Let W ⋉L be an irreducible affine Weyl group with Coxeter complex Σ, where W denotes the associated finite Weyl group and L the translation subgroup. The Steinberg torus is the simplicial complex obtained by taking the quotient of Σ by the lattice L. We show that the ordinary and flag h-polynomials of the Steinberg torus (with the empty face deleted) are generating functions over W for a descen...

The assessment of inoperability of bronchial carcinoma by angiocardiography has received little attention in this country, and it is the purpose of this paper to discuss the value of this investigation by analysing our results in 31 cases at Leicester Chest Unit. Since the introduction of angiocardiography by Robb and Steinberg in 1938 many authors have described its use in the differential dia...

Let G = GLn(q) be the general linear group of degree n ≥ 2 defined over a finite field Fq of characteristic p. We fix a prime l 6= p and let stand R for a local principal ideal domain having characteristic 0, maximal ideal lR, and containing a primitive p-th root of unity. Then the residue field K = R/lR has characteristic l and a primitive p-th root of unity. By a Steinberg lattice of G over R...