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http://dx.doi.org/10.4134/BKMS.2012.49.2.353

A NOTE ON PSEUDO-RIEMANNIAN ASSOCIATIVE FERMIONIC NOVIKOV ALGEBRAS  

Chen, Zhiqi (School of Mathematical Sciences and LPMC Nankai University)
Zhu, Fuhai (School of Mathematical Sciences and LPMC Nankai University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 353-358 More about this Journal
Abstract
In this paper, we focus on pseudo-Riemannian associative fermionic Novikov algebras. We prove that the underlying Lie algebras of pseudo-Riemannian associative fermionic Novikov algebras are 2-step nilpotent and that pseudo-Riemannian associative fermionic Novikov algebras are 3-step nilpotent. Moreover, we construct a pseudo-Riemannian associative fermionic Novikov algebra in dimension 14, which is not a Novikov algebra. It implies that the inverse proposition of Corollary 2 in the paper "Pseudo-Riemannian Novikov algebras" [J. Phys. A: Math. Theor. 41 (2008), 315207] does not hold.
Keywords
Novikov algebra; fermionic Novikov algebra; pseudo-Riemannian Lie algebra;
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