Advances in Theoretical and Mathematical Physics

Volume 8 (2004)

Number 4

Addendum: Generalized Spencer Cohomology and Filtered Deformations of Z-graded Lie Superalgebras

Pages: 697 – 709



Shun-Jen Cheng

Victor Kac


In [K]all the possibilities for the non-positive part \G_{\le 0}=\bigoplus_{j=-h}^{0}\G_{j} of the associated graded Lie superalgebra \G=\bigoplus_{j\ge -h}\G_j of a simple linearly compact Lie superalgebra L, for a "good" choice of its filtration, were obtained. In [CK2] the transitive {\mathbb Z-graded \G with those\G_{\le 0} were classified, and in [CK1] and [K], in order to reconstruct L from \G, their filtered deformations were classified. However, some cases had been inadvertently omitted. In this note we take the opportunity to amend this.

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