#### 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 $\mathfrak{g}$ 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 $\mathfrak{g}\left(R\right)$ are in natural bijection with the maximal ideals of $R$. When $\mathfrak{g}$ is a Lie algebra, we use this to give a complete classification of the finite-dimensional simple modules over twisted forms of $\mathfrak{g}\left(R\right)$.

##### Keywords
Galois descent, maximal ideals, finite-dimensional modules, multiloop algebras, twisted forms
##### Mathematical Subject Classification 2010
Primary: 17B10
Secondary: 17B67, 12G05, 17A60