Feb 2, 2011 - 9 = 9(&, II, /?)) with respect to X The Lie superalgebra 9(£, 77, /?) is called the Kac-Moody Lie superalgebra. Van de Leur [VdLl-2] classified ...
Publ. RIMS, Kyoto Univ. 35 (1999), 321-390
On Defining Relations of Affine Lie Superalgebras and Affine Quantized Universal Enveloping Superalgebras By
Hiroyuki
YAMANE
Introduction 0.1. In this paper, we give defining relations satisfied by the Chevalley generators H^Jtif, Ei9 Ft (04, n=even), (n>l, 0 < m < n , 2m (n>2,n= even) ,
(ii = 3), (n=4) f (n = 3).
In §4 and §5, we state and prove a Serre-type theorem for the affine Lie superalgebra 9 = 9(£, IT, /?). In other words, we get defining relations of 9 satisfied by the Chevalley generators (Theorem 4.5.1, Theorem 5.1.1, Theorem 5.2.1 and Theorem 5.3.1). 0.3o We are going to give an outline how we get the defining relations of 9 =
