Simple Birational Extensions of the Polynomial Algebra

Universal Central Extension of Current Superalgebras

Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras  are very impo...

ar X iv : m at h / 03 09 12 5 v 1 [ m at h . A G ] 7 S ep 2 00 3 Birational morphisms of the plane

Let A be the affine plane over a field K of characteristic 0. Birational morphisms of A are mappings A → A given by polynomial mappings φ of the polynomial algebra K[x, y] such that for the quotient fields, one has K(φ(x), φ(y)) = K(x, y). Polynomial automorphisms are obvious examples of such mappings. Another obvious example is the mapping τx given by x → x, y → xy. For a while, it was an open...

Polynomial Ore Extensions of Baer and p.p.-Rings

Polynomial Growth for Birational Mappings from Four-State Spin Edge Models

We classify all four-state spin edge models according to their behavior under a specific group of birational symmetry transformations generated from the so-called inversion relations. This analysis uses the measure of complexity of the action of birational symmetries of these lattice models, and aims at uncovering (star-triangle) solvable ones. One finds that these spin edge models have biratio...

Multivariable Dimension Polynomials and New Invariants of Differential Field Extensions

We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin’s theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension. 2000 Mathematics Subject Classification. 12H05, 12H20, 13N15.