Novikov superalgebras with $A_0=A_1A_1$
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 903-907 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $A_0=A_1A_1$.
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 $A_0=A_1A_1$.
Classification : 17A30, 17A70
Keywords: Novikov algebra; Novikov superalgebra; type $N$; type $S$
@article{CMJ_2010_60_4_a1,
     author = {Zhu, Fuhai and Chen, Zhiqi},
     title = {Novikov superalgebras with $A_0=A_1A_1$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {903--907},
     year = {2010},
     volume = {60},
     number = {4},
     mrnumber = {2738955},
     zbl = {1224.17010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a1/}
}
TY  - JOUR
AU  - Zhu, Fuhai
AU  - Chen, Zhiqi
TI  - Novikov superalgebras with $A_0=A_1A_1$
JO  - Czechoslovak Mathematical Journal
PY  - 2010
SP  - 903
EP  - 907
VL  - 60
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a1/
LA  - en
ID  - CMJ_2010_60_4_a1
ER  - 
%0 Journal Article
%A Zhu, Fuhai
%A Chen, Zhiqi
%T Novikov superalgebras with $A_0=A_1A_1$
%J Czechoslovak Mathematical Journal
%D 2010
%P 903-907
%V 60
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a1/
%G en
%F CMJ_2010_60_4_a1
Zhu, Fuhai; Chen, Zhiqi. Novikov superalgebras with $A_0=A_1A_1$. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 903-907. http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a1/

[1] Balinskii, A. A., Novikov, S. P.: Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras. Sov. Math. Dokl. 32 (1985), 228-231. | MR | Zbl

[2] Gel'fand, I. M., Dorfman, I. Ya.: Hamiltonian operators and algebraic structures related to them. Funct. Anal. Appl. 13 (1980), 248-262. | DOI | Zbl

[3] Gel'fand, I. M., Dorfman, I. Y.: The Schouten brackets and Hamiltonian operators. Funct. Anal. Appl. 14 (1981), 223-226. | DOI | MR

[4] Gel'fand, I. M., Dorfman, I. Y.: Hamiltonian operators and infinite-dimensional Lie algebras. Funct. Anal. Appl. 15 (1982), 173-187. | DOI | MR | Zbl

[5] Kac, V. G.: Vertex Algebras for Beginners. University Lecture Series, 10. American Mathematical Society (AMS) Providence (1998). | MR

[6] Kang, Y. F., Chen, Z. Q.: Novikov superalgebras in low dimensions. J. Nonlinear Math. Phys 16 (2009), 251-257. | DOI | MR

[7] Xu, X. P.: Quadratic conformal superalgebras. J. Algebra 231 (2000), 1-38. | DOI | MR | Zbl

[8] Xu, X. P.: Introduction to Vertex Operator Superalgebras and Their Modules. Kluwer Dordercht (1998). | MR | Zbl

[9] Xu, X. P.: Hamiltonian operators and associative algebras with a derivation. Lett. Math. Phys. 33 (1995), 1-6. | DOI | MR | Zbl

[10] Xu, X. P.: Hamiltonian superoperators. J. Phys A. Math. Gen. 28 (1995), 1681-1698. | MR | Zbl