Algebras with pseudo-Riemannian bilinear forms
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The purpose of this paper is to study pseudo-Riemannian al-gebras, which are algebras with pseudo-Riemannian non-degenerate sym-metric bilinear forms. We find that pseudo-Riemannian algebras whose left centers are isotropic play a curial role and show that the decomposi-tion of pseudo-Riemannian algebras whose left centers are isotropic into indecomposable non-degenerate ideals is unique up to a special automor-phism. Furthermore, if the left center equals the center, the orthogonal decomposition of any pseudo-Riemannian algebra into indecomposable non-degenerate ideals is unique up to an isometry.
Abstract
The purpose of this paper is to study pseudo-Riemannian al-gebras, which are algebras with pseudo-Riemannian non-degenerate sym-metric bilinear forms. We find that pseudo-Riemannian algebras whose left centers are isotropic play a curial role and show that the decomposi-tion of pseudo-Riemannian algebras whose left centers are isotropic into indecomposable non-degenerate ideals is unique up to a special automor-phism. Furthermore, if the left center equals the center, the orthogonal decomposition of any pseudo-Riemannian algebra into indecomposable non-degenerate ideals is unique up to an isometry.
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