The Minkowski group (Q793976)

The author investigates the length problem in Euclidean and Minkowskian vector spaces, i.e. spaces V with dim \(V\geq 3\) and \(\dim Rad(V)=1\). Let \(g\in 0^+(V)\), the Minkowskian group of V, then \(g=h_ 1h_ 2...h_ s\), where the \(h_ i\) are halfturns. The author determines the minimal number s as a function of dim B(g), where \(B(g)=\{v^ g-v| v\in V\}=\) the path of g. The proofs depend heavily on the results of the author's paper in Abh. Math. Semin. Univ. Hamb. 46, 97-127 (1978; Zbl 0367.50002).