Determination of the automorphism group of a hyperbolic K-loop

Abstract

To each commutative Euclidean field (K, +, ·) there corresponds, via Hermitian matrices, a Minkowski-Space-Time-World (H,K, →), a hyperbolic space (H1+, C) and a K-loop (H1+, ⊕). The set H1+ of points of the hyperbolic space can be turned in a K-loop, and conversely, the incidence structure of the hyperbolic space can be reconstructed from the K-loop. Therefore we call such K-loops hyperbolic. The automorphism group of a hyperbolic K-loop will be determined. The main result is stated in Theorem 1.