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… 

On universal conformal envelopes for quadratic conformal algebras

We prove that every quadratic Lie conformal algebra constructed on a special Gel’fand–Dorfman algebra embeds into the universal enveloping associative conformal algebra with a locality function bound

Cohomology and deformation quantization of Poisson conformal algebras

A bstract . In this paper, we first recall the notion of (noncommutative)Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative)

Standard Bases for the Universal Associative Conformal Envelopes of Kac–Moody Conformal Algebras

We study the universal enveloping associative conformal algebra for the central extension of a current Lie conformal algebra at the locality level N = 3. A standard basis of defining relations for

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

Universal enveloping conformal algebras

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

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

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

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

On the classification of subalgebras of CendN and gcN

The classification of Novikov algebras in low dimensions

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

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