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A NOTE ON PSEUDO-RIEMANNIAN ASSOCIATIVE FERMIONIC NOVIKOV ALGEBRAS
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 Title & Authors
A NOTE ON PSEUDO-RIEMANNIAN ASSOCIATIVE FERMIONIC NOVIKOV ALGEBRAS
Chen, Zhiqi; Zhu, Fuhai;
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 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;
 Language
English
 Cited by
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