A Serre type theorem for affine Lie superalgebras and their quantized enveloping superalgebras
type: Item
instance of: scholarly article
title: A Serre type theorem for affine Lie superalgebras and their quantized enveloping superalgebras
zbMATH Open document ID: 0987.17008
author: Hiroyuki Yamane
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-08-08T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1195511169
review text: 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)].
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 597325
zbMATH Keywords: Hopf superalgebra
zbMATH Keywords: quantized enveloping algebras for Kac-Moody algebras
reviewed by: Olaf Ninnemann
MaRDI profile type: Publication
OpenAlex ID: W2045129648
cites work: Quantum R matrix for the generalized Toda system
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cites work: Q4394544
DOI: 10.3792/PJAA.70.31
description: scientific article; zbMATH DE number 597325