Overrings of primitive factors of quantum sl(2)

AbstractWe construct certain completely prime Dixmier algebras which are overrings of primitive factors of quantum sl(2). As in the classical case, these algebras are parametrized by infinitesimal characters corresponding to the half-integers. We also show that all completely prime Dixmier algebras for quantum sl(2) are essentially isomorphic to the algebras we have constructed

Equidissections of darts

We define the dart $D(a)$ to be the nonconvex quadrilateral whose vertices are $(0,1), (1,1), (1,0), (a,a)$ (in counterclockwise order), with $a>1$. Such a dart can be dissected into any even number of equal-area triangles. Here we investigate darts that can be dissected into an odd number of equal-area triangle