Vol. 7, No. 2, 2013

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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
Abstract

Given a central simple algebra g and a Galois extension of base rings SR, we show that the maximal ideals of twisted SR-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