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arxiv: 1308.4175 · v1 · pith:Z6LVFUZKnew · submitted 2013-08-19 · 🧮 math.RT · math.RA

Maximal ideals and representations of twisted forms of algebras

classification 🧮 math.RT math.RA
keywords mathfrakalgebraformsidealsmaximaltwistedsimplealgebras
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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 $\mathfrak{g}(R)$ 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 $\mathfrak{g}(R)$.

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