Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions

Wolfgang Bertram, Pierre Bieliavsky

Published 2010-11-12, updated 2012-03-05Version 2

We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an elementary way by using associative algebras with several involutions. This construction shows a remarkable duality between the underlying "space" and the "deformation parameter".