Maximal ideals and representations of twisted forms of algebras

Abstract

Abstract Given a central simple algebra g g and a Galois extension of base rings S ∕ R S∕R, we show that the maximal ideals of twisted S ∕ R S∕R-forms of the algebra of currents g ( R ) g(R) are in natural bijection with the maximal ideals of R R. When g 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 ) g(R).