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Start Over Subject Novikov algebra

1. Novikov superalgebras with $A_0=A_1A_1$.

Creator:
Zhu, Fuhai and Zhiqi
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Novikov algebra, Novikov superalgebra, type $N$, and type $S$
Language:
English
Description:
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 $A_0=A_1A_1$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Underlying Lie algebras of quadratic Novikov algebras

Creator:
Chen, Zhiqi
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Novikov algebra, quadratic Novikov algebra, and underlying Lie algebra
Language:
English
Description:
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and the Hamiltonian operators in formal variational calculus. In this note we prove that the underlying Lie algebras of quadratic Novikov algebras are 2-step nilpotent. Moreover, we give the classification up to dimension $10$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public