We construct, for q a root of unity of odd order, an embedding of the projective special linear group PSL(n) into the group of bi-Galois objects over uq(sl(n)) ∗, the coordinate algebra of the Frobenius-Lusztig kernel of SL(n), which is shown to be an isomorphism at n = 2.

This paper examines abstract regular polytopes whose automorphism group is the projective special linear group PSLp4,Fqq. For q odd we show that polytopes of rank 4 exist by explicitly constructing PSLp4,Fqq as a string C-group of that rank. On the other hand, we show that no abstract regular polytope exists whose group of automorphisms is PSLp4,F2k q.

Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, projective minimal surfaces, and other classical soliton surfaces. Completely integrable equations suc...

Abstract. We consider the action of the 2-dimensional projective special linear group PSL(2, q) on the projective line PG(1, q) over the finite field Fq, where q is an odd prime power. A subset S of PSL(2, q) is said to be an intersecting family if for any g1, g2 ∈ S, there exists an element x ∈ PG(1, q) such that x1 = x2 . It is known that the maximum size of an intersecting family in PSL(2, q...