Maximal ideals and representations of twisted forms of algebras

Lau, Michael; Pianzola, Arturo

doi:10.2140/ant.2013.7.431

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Maximal ideals and representations of twisted forms of algebras

Michael Lau and Arturo Pianzola

Vol. 7 (2013), No. 2, 431–448

DOI: 10.2140/ant.2013.7.431

Abstract

Given a central simple algebra $g$ and a Galois extension of base rings $S ∕ R$ , we show that the maximal ideals of twisted $S ∕ R$ -forms of the algebra of currents $g (R)$ are in natural bijection with the maximal ideals of $R$ . When $g$ is a Lie algebra, we use this to give a complete classification of the finite-dimensional simple modules over twisted forms of $g (R)$ .

Keywords

Galois descent, maximal ideals, finite-dimensional modules, multiloop algebras, twisted forms

Mathematical Subject Classification 2010

Primary: 17B10

Secondary: 17B67, 12G05, 17A60

Milestones

Received: 7 November 2011

Accepted: 3 March 2012

Published: 25 April 2013

Authors

Michael Lau
Département de mathématiques et de statistique Université Laval Pavillon Vachon (Local 1056) 1045 av. de la Médecine Québec, QC G1V0A6 Canada

Arturo Pianzola
Department of Mathematical and Statistical Sciences University of Alberta 632 Central Academic Building Edmonton, AB T6G2G1 Canada	Centro de Altos Estudios en Ciencias Exactas Avenida de Mayo 866, (1084) Buenos Aires Argentina

Vol. 7, No. 2, 2013