ALGEBRAS WITH PSEUDO-RIEMANNIAN BILINEAR FORMS

作者：Chen Zhiqi^*; Liang Ke; Zhu Fuhai

来源：Journal of the Korean Mathematical Society, 2011, 48(1): 1-12.

DOI：10.4134/JKMS.2011.48.1.001

• pseudo-Riemannian algebra
• indecomposable ideal
• isometry
• orthogonal decomposition

The purpose of this paper is to study pseudo-Riemannian algebras, which are algebras with pseudo-Riemannian non-degenerate symmetric bilinear forms. We find that pseudo-Riemannian algebras whose left centers are isotropic play a curial role and show that the decomposition of pseudo-Riemannian algebras whose left centers are isotropic into indecomposable non-degenerate ideals is unique up to a special automorphism. 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.

• 出版日期2011-1
• 单位南开大学