A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Understanding the exceptional Lie groups as the symmetry groups of simpler objects is a long-standing program in mathematics. Here, we explore one famous realization of the smallest exceptional Lie group, G2. Its Lie algebra acts locally as the symmetries of a ball rolling on a larger ball, but only when the ratio of r…
We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic) projective plane, the octonionic projective plane of indefinite signature, and the hyperbolic dual of the octonionic projective plane; we di…
New symmetry found in 8D distribution with 6D square.
We show that any dimension nearly Kähler (or nearly para-Kähler) geometry arises as a projective manifold equipped with a holonomy reduction. In the converse direction we show that if a projective manifold is equipped with a parallel -dimensional cross product on its standard tractor bundle …
Explicit BCH series radii found for special Banach-Malcev shift algebras.