Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2010.11.02
  • Published : 2012.03.31
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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.

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References

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