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ALGEBRAS WITH PSEUDO-RIEMANNIAN BILINEAR FORMS

  • Chen, Zhiqi (SCHOOL OF MATHEMATICAL SCIENCES AND LPMC NANKAI UNIVERSITY) ;
  • Liang, Ke (SCHOOL OF MATHEMATICAL SCIENCES AND LPMC NANKAI UNIVERSITY) ;
  • Zhu, Fuhai (SCHOOL OF MATHEMATICAL SCIENCES AND LPMC NANKAI UNIVERSITY)
  • Received : 2007.11.14
  • Accepted : 2010.03.03
  • Published : 2011.01.01

Abstract

The purpose of this paper is to study pseudo-Riemannian algebras, which are algebras with pseudo-Riemannian non-degenerate symmetric bilinear forms. We nd 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.

Keywords

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

Acknowledgement

Supported by : National Natural Science Foundation of China

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