We present a classification of the hyperbolic Kac–Moody (HKM) superalgebras. The HKM superalgebras of rank r ≥ 3 are finite in number (213) and limited in rank (6). The Dynkin–Kac diagrams and the corresponding simple root systems are determined. We also discuss a class of singular sub(super)algebras obtained by a folding procedure. MSC number: 17B65, 17B67 LAPTH-1068/04 DSF-TH-28/04 math-ph/04...

Background/introduction The biologic dose response curves of thermal dose and absorbed radiation dose have not been compared to each other even though they have both been extensively investigated separately and combined. Although heat and radiation produce cell kill by different biological mechanisms (Thermal dose denatures proteins and the radiation dose causes DNA damage) a comparison of dose...

In this paper, we study the existence of a skew Killing spinor (see the definition below) on 2 and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.