Errata to “On Defining Relations of Affine Lie Superalgebras and Affine Quantized Universal Enveloping Superalgebras”

1 Preliminary. Keep the notation and terminology of [1]. We say that the datum (E,Π, p) is of (A(1, 1)(1))H type if (E,Π, p) is of affine ABCD type (see Definition 1.4.1), Π = {α0, α1, α2, α3} and if the Dynkin diagram of (E,Π, p) is either of the two Dynkin diagrams of (1). Until the end of this section, we assume that (E,Π, p) is of (A(1, 1)(1))H type. Then G(E,Π, p) ∼= (A(1, 1)(1))H, G (E,Π, p) ∼= (sl(2, 2)(1))H, and Φ(E,Π, p) = {±(m+1)δ, ±(mδ+αi), ±(mδ+ αi + αi−1), ±(mδ + αi + αi−1 + αi−2)|i = 0, 1, 2, 3 ∈ Z/4Z, m ≥ 0}. (See Subsections 1.5 and 3.5, and notice that (A(1, 1)(1))H and A(1, 1) (resp. (sl(2, 2)(1))H and sl(2, 2)) are not the same; however they are closely related.) Define E i , E (m) ii−1, E (m) ii−1i−2 ∈ N+(⊂ G(E,Π, p)) (i ∈ Z/4Z,m ≥ 0) inductively by E i = Ei, E (m) i = [Ei, [Ei−1, E (m−1) i−2i−3i]], E (m) ii−1 = [Ei, E (m) i−1 ], E (m) ii−1i−2 = [Ei, E (m) i−1i−2]. Let Eii−1 = E (0) ii−1 and Eii−1i−2 = E (0) ii−1i−2. Let x : N+ → N− be the isomorphism such that x(Ei) = Fi (0 ≤ i ≤ 3). Denote (E,Π, p) by (AA) if its Dynkin diagram is the left one of (1) and if