Flat manifolds with holonomy representation of quaternionic type

Communications in Algebra, vol. 49, pp. 1286–1294

Abstract

We are interested in the question of the existence of flat manifolds for which all R-irreducible components of the holonomy representation are either absolutely irreducible, of complex or of quaternionic type. In the first two cases such examples are well known. But the existence of the third type of flat manifolds was unknown to the authors. In this article, we construct such an example. Moreover, we present a list of finite groups for which a construction of manifolds of quaternionic type is impossible.

Authors 3

1. Gerhard Hiß Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Aachen, Germany

2. Rafał Lutowski corresponding

   University of Gdańsk

   Affiliation as printed

   Institute of Mathematics, University of Gdańsk, Gdańsk, Poland

   Institute of Mathematics, University of Gdánsk, Gdánsk, Poland

3. Andrzej Szczepański

   University of Gdańsk

   Affiliation as printed

   Institute of Mathematics, University of Gdańsk, Gdańsk, Poland

   Institute of Mathematics, University of Gdánsk, Gdánsk, Poland