Pseudo-symmetric pairs for Kac-Moody algebras

Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces real forms of complex algebras, are well-studied in the context symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, introduce concept pseudo-involution, an automorphism which is only required act involutively on stable Cartan subalgebra, pseudo-fixed-point natural substitute for subalgebra. setting, comprehensive discussion pseudo-involutions second kind, associated subalgebras, restricted root systems Weyl groups, terms generalizations Satake diagrams.