A Serre type theorem for affine Lie superalgebras and their quantized enveloping superalgebras
This is an announcement of results proved in Publ. Res. Inst. Math. Sci. 30, 15--87 (1994; Zbl 0821.17005). The author states some `super' versions of Drinfeld-Jimbo results on quantized enveloping algebras for Kac-Moody algebras. His main result gives a construction of a topologically free Hopf superalgebra \(U_h({\mathfrak g})\), for each affine Lie superalgebra \({\mathfrak g}\), over the formal power series algebra \(\mathbb Ch \) with \((h)\)-adic topology that turns into the universal enveloping superalgebra \(U({\mathfrak g})\) as \(h\to 0\). Finally the author studies a nondegenerate \(\mathbb Ch \)-bilinear form on the product of the positive and negative Borel-type Hopf subsuperalgebas of \(U_h({\mathfrak g})\) having analogous properties given by \textit{V. G. Drinfeld} in the purely even case [see Proc. Int. Congr. Math., Berkeley 1986, Vols. 1, 2, 798--820 (1987; Zbl 0667.16003)].
quantized enveloping algebras for Kac-Moody algebras
scientific article; zbMATH DE number 597325