Projectively simple rings

We introduce the notion of a projectively simple ring, which is an infinite-dimensional graded k-algebra A such that every 2-sided ideal has finite codimension in A (over the base field k). Under some (relatively mild) additional assumptions on A, we reduce the problem of classifying such rings (in the sense explained in the paper) to the following geometric question, which we believe to be of independent interest. Let X is a smooth irreducible projective variety. An automorphism f: X -> X is called wild if it X has no proper f-invariant subvarieties. We conjecture that if X admits a wild automorphism then X is an abelian variety. We prove several results in support of this conjecture; in particular, we show that the conjecture is true if X is a curve or a surface. In the case where X is an abelian variety, we describe all wild automorphisms of X. In the last two sections we show that if A is projectively simple and admits a balanced dualizing complex, then Proj(A) is Cohen-Macaulay and Gorenstein.Comment: Some new material has been added in Section 1; to appear in Advances in Mathematic

Electronic structure of Ba(Fe,Ru)2As2 and Sr(Fe,Ir)2As2 alloys

The electronic structures of Ba(Fe,Ru)$_2$As$_2$ and Sr(Fe,Ir)$_2$As$_2$ are investigated using density functional calculations. We find that these systems behave as coherent alloys from the electronic structure point of view. In particular, the isoelectronic substitution of Fe by Ru does not provide doping, but rather suppresses the spin density wave characteristic of the pure Fe compound by a reduction in the Stoner enhancement and an increase in the band width due hybridization involving Ru. The electronic structure near the Fermi level otherwise remains quite similar to that of BaFe$_{2}$As$_{2}$. The behavior of the Ir alloy is similar, except that in this case there is additional electron doping

Primitive Cohomology of Hopf algebras

Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented. Firstly we classify all non locally PI, pointed Hopf algebra domains of Gelfand-Kirillov dimension two; and secondly we classify all pointed Hopf algebras of rank one. The first classification extends some results of Brown, Goodearl and others in an ongoing project to understand all Hopf algebras of low Gelfand-Kirillov dimension. The second generalizes results of Krop-Radford and Wang-You-Chen which classified Hopf algebras of rank one under extra hypothesis. Properties and algebraic structures of the primitive cohomology are discussed