Maria Gorelik: Kac-Moody superalgebras

I will review results of C. Hoyt and V. Serganova on classification of Kac-Moody superalgebras. In supercase several Cartan matrices may determine the same superalgebra and our definition of Kac-Moody superalgebra is based on this fact. Surprisingly, all symmetrizable indecomposable Kac-Moody superalgebras with isotropic roots are finite-dimensional or affine. I will discuss a notion of integrable modules over Kac-Moody superalgebras.