Embedding of simply laced hyperbolic Kac-Moody superalgebras

Abstract

We show that HD(4, 1) hyperbolic Kac-Moody superalgebra of rank 6 contains every simply laced Kac-Moody superalgebra with degenerate odd root as a Lie subalgebra. Our result is the supersymmetric extension of earlier work [S. Viswanath, “Embeddings of HyperbolicKac-Moody Algebras into E10,” Lett. Math. Phys. 83, 139–148 (2008)]10.1007/s11005-007-0214-7 for hyperbolic Kac-Moody algebra.

The trascendence of Kac-Moody algebras

“…In 2015, B. Ransingh dealt with Vogan diagrams of untwisted affine Kac-Moody superalgebras [212], S. Nayak and K.C. Pati studied the embedding of simply laced hyperbolic Kac-Moody superalgebras [196], D. Hill and W. Wang dealt with the categorification of quantum Kac-Moody superalgebras [122] and S.J. Cheng, J.H.…”