JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ALGEBRAS WITH PSEUDO-RIEMANNIAN BILINEAR FORMS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ALGEBRAS WITH PSEUDO-RIEMANNIAN BILINEAR FORMS
Chen, Zhiqi; Liang, Ke; Zhu, Fuhai;
  PDF(new window)
 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;
 Language
English
 Cited by
 References
1.
A. Aubert and A. Medina, Groupes de Lie pseudo-riemanniens plats, Tohoku Math. J. (2) 55 (2003), no. 4, 487-506. crossref(new window)

2.
M. Bordemann, Nondegenerate invariant bilinear forms on nonassociative algebras, Acta Math. Univ. Comenian. (N.S.) 66 (1997), no. 2, 151-201.

3.
M. Boucetta, Poisson manifolds with compatible pseudo-metric and pseudo-Riemannian Lie algebras, Differential Geom. Appl. 20 (2004), no. 3, 279-291. crossref(new window)

4.
Z. Chen and F. Zhu, Bilinear forms on fermionic Novikov algebras, J. Phys. A 40 (2007), no. 18, 4729-4738. crossref(new window)

5.
G. Favre and L. J. Santharoubane, Symmetric, invariant, nondegenerate bilinear form on a Lie algebra, J. Algebra 105 (1987), no. 2, 451-464. crossref(new window)

6.
J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293-329. crossref(new window)

7.
A. A. Sagle, Nonassociative algebras and Lagrangian mechanics on homogeneous spaces, Algebras Groups Geom. 2 (1985), no. 4, 478-494.

8.
F. Zhu and L. Zhu, The uniqueness of the decomposition quadratic Lie algebras, Comm. Algebra 29 (2001), no. 11, 5145-5154. crossref(new window)