7 feb 2017 -- 15:00
Aula 3, Dipartimento di Matematica, Università di Torino
Abstract.
We give a short review of the construction of homogeneous hypercomplex manifolds, proposed by physicists Ph.Spindel, A. Servin, W. Troost and A. Van Proyen and studied and generalized to homogeneous quaternionic manifolds by D. Joyce and then by L.Bedulli, A.Gori and F. Podesta. It is based on iteration of the construction of Wolf symmetric spaces and is naturally extended to para-case. We consider another construction of (para)quaternionic and (para)homogeneous (not necessary compact) manifolds of a semisimple Lie group, based on theory of $sl_2$-modules. A relation between some class of homogeneous (para)quaternionic manifolds, 5-graded Lie algebras of contact type and Kantor pairs will be also discussed.