A NOTE ON PSEUDO-RIEMANNIAN ASSOCIATIVE FERMIONIC NOVIKOV ALGEBRAS
A NOTE ON PSEUDO-RIEMANNIAN ASSOCIATIVE FERMIONIC NOVIKOV ALGEBRAS
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DOI：
10.4134/bkms.2012.49.2.353
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发表时间：
2012-03
影响因子：
0.5
通讯作者：
Zhiqi Chen;Fuhai Zhu
中科院分区：
文献类型：
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作者：
Zhiqi Chen;Fuhai Zhu
本文主要研究伪黎曼结合费米子Novikov代数。证明了伪黎曼结合费米子Novikov代数的底层李代数是2步幂零的，伪黎曼结合费米子Novikov代数是3步幂零的.此外，我们构造了一个14维的伪黎曼结合费米子Novikov代数，它不是Novikov代数。这意味着“伪黎曼Novikov代数”[J. Phys. A：Math. Theor. 41（2008），315207]不成立。
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.