# Quadratic Lie conformal superalgebras related to Novikov superalgebras

@article{Kolesnikov2019QuadraticLC, title={Quadratic Lie conformal superalgebras related to Novikov superalgebras}, author={Pavel Kolesnikov and Roman Kozlov and A. S. Panasenko}, journal={Journal of Noncommutative Geometry}, year={2019} }

We study quadratic Lie conformal superalgebras associated with No\-vikov superalgebras. For every Novikov superalgebra $(V,\circ)$, we construct an enveloping differential Poisson superalgebra $U(V)$ with a derivation $d$ such that $u\circ v = ud(v)$ and $\{u,v\} = u\circ v - (-1)^{|u||v|} v\circ u$ for $u,v\in V$. The latter means that the commutator Gelfand--Dorfman superalgebra of $V$ is special. Next, we prove that every quadratic Lie conformal superalgebra constructed on a finite…

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## References

SHOWING 1-10 OF 41 REFERENCES

### Dorfman

- Hamilton operators and associated algebraic structures, Functional analysis and its application 13
- 1979

### Gelfand–Dorfman algebras, derived identities, and the Manin product of operads

- MathematicsJournal of Algebra
- 2019

### Universal enveloping conformal algebras

- Mathematics
- 2000

Abstract. The main objective of this paper is to study embeddings of Lie conformal algebras into associative conformal algebras. We prove that not all Lie conformal algebras admit such embeddings.…

### Vertex algebras for beginners

- Mathematics
- 1997

Preface. 1: Wightman axioms and vertex algebras. 1.1: Wightman axioms of a QFT. 1.2: d = 2 QFT and chiral algebras. 1.3: Definition of a vertex algebra. 1.4: Holomorphic vertex algebras. 2: Calculus…

### Hamiltonian operators and related differential-algebraic Balinsky-Novikov, Riemann and Leibniz type structures on nonassociative noncommutative algebras

- MathematicsProceedings of the International Geometry Center
- 2019

We review main differential-algebraic structures \ lying in background of \ analytical constructing multi-component Hamiltonian operators as derivatives on suitably constructed loop Lie algebras,…

### Examples of Algebraic Operads

- Mathematics
- 2012

In Chap. 9, we studied in detail the operad Ass encoding the associative algebras. It is a paradigm for nonsymmetric operads, symmetric operads, cyclic operads. In this chapter we present several…

### The classification of Novikov algebras in low dimensions

- Mathematics
- 2001

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in the formal variational calculus. For further our understanding and physical…

### PBW-Pairs of Varieties of Linear Algebras

- Mathematics
- 2014

The notion of a Poincaré–Birkhoff–Witt (PBW)-pair of varieties of linear algebras over a field is under consideration. Examples of PBW-pairs are given. We prove that if (𝒱, 𝒲) is a PBW-pair and the…