Almost complex structures on k-symmetric spaces

The notion of canonical almost complex structure on a homogeneous k-symmetric space of a Lie group G has been introduced by Joseph Wolf and Alfred Gray . This work is devoted to the study of some necessary and sufficient conditions to the integrability of such an almost complex structure. The conjugation classes of order k elements of a Lie group G are examples of homogeneous k-symmetric spaces; we give special attention to those spaces and use them to study the general case.