Zhu, Fuhai; Chen, Zhiqi Novikov superalgebras with \(A_0=A_1A_1\). (English) Zbl 1224.17010 Czech. Math. J. 60, No. 4, 903-907 (2010). Summary: Novikov superalgebras are related to quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play a fundamental role in completely integrable systems. In this note we show that the Novikov superalgebras with \(A_0=A_1A_1\) and \(\dim A_1=2\) are of type \(N\) and give a class of Novikov superalgebras of type \(S\) with \(A_0=A_1A_1\). Cited in 3 Documents MSC: 17A70 Superalgebras 17A30 Nonassociative algebras satisfying other identities Keywords:Novikov algebra; Novikov superalgebra; type \(N\); type \(S\) PDFBibTeX XMLCite \textit{F. Zhu} and \textit{Z. Chen}, Czech. Math. J. 60, No. 4, 903--907 (2010; Zbl 1224.17010) Full Text: DOI EuDML References: [1] A.A. Balinskii, S. P. Novikov: Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras. Sov. Math. Dokl. 32 (1985), 228–231. · Zbl 0606.58018 [2] I.M. Gel’fand, I. Ya. Dorfman: Hamiltonian operators and algebraic structures related to them. Funct. Anal. Appl. 13 (1980), 248–262. · Zbl 0437.58009 [3] I.M. Gel’fand, I.Y. Dorfman: The Schouten brackets and Hamiltonian operators. Funct. Anal. Appl. 14 (1981), 223–226. · Zbl 0455.58013 [4] I.M. Gel’fand, I.Y. Dorfman: Hamiltonian operators and infinite-dimensional Lie algebras. Funct. Anal. Appl. 15 (1982), 173–187. · Zbl 0487.58008 [5] V.G. Kac: Vertex Algebras for Beginners. University Lecture Series, 10. American Mathematical Society (AMS), Providence, 1998. [6] Y.F. Kang, Z.Q. Chen: Novikov superalgebras in low dimensions. J. Nonlinear Math. Phys 16 (2009), 251–257. · Zbl 1232.17011 [7] X.P. Xu: Quadratic conformal superalgebras. J. Algebra 231 (2000), 1–38. · Zbl 1001.17024 [8] X.P. Xu: Introduction to Vertex Operator Superalgebras and Their Modules. Kluwer, Dordercht, 1998. · Zbl 0929.17030 [9] X.P. Xu: Hamiltonian operators and associative algebras with a derivation. Lett. Math. Phys. 33 (1995), 1–6. · Zbl 0837.16034 [10] X.P. Xu: Hamiltonian superoperators. J. Phys A. Math. Gen. 28 (1995), 1681–1698. · Zbl 0852.58043 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.