Supersymmetry algebra cohomology II: Primitive elements in 2 and 3 dimensions

The primitive elements of the supersymmetry algebra cohomology as defined in a companion paper are computed exhaustively for standard supersymmetry algebras in dimensions D=2 and D=3, for all signatures (t,D-t) and all numbers N of sets of supersymmetries.Comment: 19 pages; v3: matches published version; presentation of D=3 analysis streamlined; presentation of lemmas 2.3 and 2.5 improved; minor correction of misprints; minor change of titl

B\"acklund Transformations an Zero-Curvature Representations of Systems of Partial Differential Equations

It is shown that B\"acklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs.Comment: 25 page

On the Proper Setup of the Double Mach Reflection as a Test Case for the Resolution of Gas Dynamics Codes

This note discusses the initial and boundary conditions as well as the size of the computational domain for the double Mach reflection problem when set up as a test for the resolution of an Euler scheme for gas dynamics

Jet coordinates for local BRST cohomology

The construction of appropriate jet space coordinates for calculating local BRST cohomology groups is discussed. The relation to tensor calculus is briefly reviewed too.Comment: 11 pages, correction in eq. (29), to appear in Lett.Math.Phy