Loop algebras of Zassenhaus algebras in characteristic three
type: Item
instance of: scholarly article
title: Loop algebras of Zassenhaus algebras in characteristic three
zbMATH Open document ID: 0966.17013
DOI: 10.1007/BF02808175
published in: Israel Journal of Mathematics
publication date: 2000-12-18T00:00:00Z
review text: The author continues the investigation of the central extensions of some loop algebras of Zassenhaus algebras over fields of characteristic \(p\). In this paper the case \(p=3\) is considered. When \(p=3\) the Zassenhaus algebra \(W=W(1;n)\) has an invariant symmetrical form, which allows to construct the infinite series of independent 2-cocycles (loop cocycles) on a special loop algebra \(L\) of \(W\) using cyclic 2-cohomology of the polynomial algebra \(\mathbb F_p[t]\). The description of 2-cocycles of Zassenhaus algebra obtained earlier by \textit{A. S. Dzhumadil'daev} [Mat. Sb., Nov. Ser. 126(168), 473-489 (1985); English transl. in Math. USSR, Sb. 54, 457-474 (1986; Zbl 0574.17009)] and \textit{R. Farnsteiner} [Can. J. Math. 39, 1078-1106 (1987; Zbl 0631.17005)] is given by means of which the infinite series of independent cocycles on loop algebra \(L\) (finite cohomology cocyles) can be constructed naturally. It is proved that the infinite dimensional central extension constructed by means of finite cohomology cocycles and loop cocycles is finitely presented. Generators and defining relations are indicated.
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B60
Mathematics Subject Classification ID: 17B68
zbMATH DE Number: 1310632
zbMATH Keywords: loop algebra
zbMATH Keywords: Zassenhaus algebra
zbMATH Keywords: cohomology
zbMATH Keywords: central extension
zbMATH Keywords: finite presentability
author: Andrea Caranti
reviewed by: Michael Kuznetsov
MaRDI profile type: Publication
cites work: Presenting the graded Lie algebra associated to the Nottingham group
cites work: Q4896962
cites work: Q3693671
cites work: The Associative Forms of the Graded Cartan Type Lie Algebras
cites work: Dual Space Derivations and H2(L, F) of Modular Lie Algebras
cites work: The arithmetic theory of loop groups
cites work: Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra
cites work: Some Remarks on Infinite Groups
cites work: Q3941589
cites work: Q4039778
cites work: Erratum and addendum to ‘‘Central extensions of current algebras”
cites work: The second homology group of current Lie algebras
description: scientific article; zbMATH DE number 1310632