English

Maximal ideals and representations of twisted forms of algebras

Representation Theory 2013-08-21 v1 Rings and Algebras

Abstract

Given a central simple algebra g\mathfrak{g} and a Galois extension of base rings S/RS/R, we show that the maximal ideals of twisted S/RS/R-forms of the algebra of currents g(R)\mathfrak{g}(R) are in natural bijection with the maximal ideals of RR. When g\mathfrak{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)\mathfrak{g}(R).

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Cite

@article{arxiv.1308.4175,
  title  = {Maximal ideals and representations of twisted forms of algebras},
  author = {Michael Lau and Arturo Pianzola},
  journal= {arXiv preprint arXiv:1308.4175},
  year   = {2013}
}

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18 pages