In this paper we study characters on special linear groups SLn(R), where R is either an infinite field or the localization of an order in a number field. We give several applications to the theory of measure-preserving actions, operator-algebraic superrigidity, and almost homomorphisms.

A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring R/IΛ and the inverse system algebra R/I∆. We give a careful study of both of these algebras. Our main results are a full description of the graded Betti numbers of both algebras in the more general setting of linear spaces (giv...

In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding ε k of an orthogonal Grassmannian ∆k. In particular, we determine some of the parameters of the codes arising from the projective system determined by ε k (∆k). We also study special sets of points of ∆k which are met by any line of ∆k in at most 2 points and we show that their imag...

In this paper we present a generic projective interior point algorithm for linear programming which includes modiied versions of Karmarkar's original algorithm and most other projective algorithms that have been proposed as special cases. We show that this class of algorithms has a worst case iteration bound of O(p nL) and is closely related to the class of potential reduction interior point me...

The projective shape of a configuration consists of the information that is invariant under projective transformations. It encodes the information about an object reconstructable from uncalibrated camera views. The space of projective shapes of k points in RP is by definition the quotient space of k copies of RP modulo the action of the projective linear group PGLpdq. A detailed examination of ...

Let G be the projective special linear group PSL(2, 2), let X be the projective line and B be any subgroup of GF ∗(2n). We give a new infinite family of simple 3-designs by determining the parameter set of (X, G(B0)), where B0 = B ∪ {0}.

The similarity between finite-dimensional projective spaces and finite abelian groups has often been noted(1); and thus one may expect that the more general features of these two theories are identical. But the likeness is more than a superficial one; and consequently it is possible to give a unified treatment for spaces and groups. It may be worthwhile to indicate in a few lines the developmen...