Related papers: Quadratic conformal superalgebras
Novikov superalgebras are related to the quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play fundamental role in the completely integrable systems. In this note, we divide Novikov superalgebras into two…
In this paper, simplicity of quadratic Lie conformal algebras are investigated. From the point view of the corresponding Gel'fand-Dorfman bialgebras, some sufficient conditions and necessary conditions to ensure simplicity of quadratic Lie…
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…
A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of…
In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra $R=\mathbb{C}[\partial]V$ through three algebraic operations on $V$ are…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional…
In this paper, we give an expansion of two notions of double extension and $T^*$-extension for quadratic and odd quadratic Lie superalgebras. Also, we provide a classification of quadratic and odd quadratic Lie superalgebras up to dimension…
A Lie algebra is said to be quadratic if it admits a symmetric invariant and non-degenerated bilinear form. Semisimple algebras with the Killing form are examples of these algebras, while orthogonal subspaces provide abelian quadatric…
A Lie superalgebra endowed with a supersymmetric, even, non-degenerate, invariant bilinear form is called a quadratic Lie superalgebra. In this paper we give inductive descriptions of quadratic Lie superalgebras in terms of generalized…
The present work studies deeply quadratic symplectic Lie superalgebras, obtaining, in particular, that they are all nilpotent. Consequently, we provide classifications in low dimensions and identify the double extensions that maintain…
By definition, a quadratic Lie superalgebra is a Lie superalgebra endowed with a non-degenerate supersymmetric bilinear form which satisfies the even and invariant properties. In this paper we calculate all of the second cohomology group of…
A list of superconformal chiral operator product expansion algebras with quadratic nonlinearity in two dimensions is completed on the basis of the known classification of little conformal Lie superalgebras. In addition to the previously…
In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and…
The notion of a Lie conformal superalgebra encodes an axiomatic descrption of singular parts of the operator product expansions of chiral fields in conformal field theory. In the paper we give a detailed proof of the classification of all…
A quadratic Novikov algebra is a Novikov algebra $(A, \circ)$ with a symmetric and nondegenerate bilinear form $B(\cdot,\cdot)$ satisfying $B(a\circ b, c)=-B(b, a\circ c+c\circ a)$ for all $a$, $b$, $c\in A$. This notion appeared in the…
In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use this method to obtain the algebraic classification of complex…
We list classical spherical subalgebras in basic matrix Lie superalgebras which are quantizable to coideal subalgebras in the standard quantum supergroups, for any choice of Borel subalgebra. We classify the corresponding Satake-type…
We define a new invariant of quadratic Lie algebras and give a complete study and classification of singular quadratic Lie algebras, i.e. those for which the invariant does not vanish. The classification is related to…
We explicitly compute the automorphism group of the large N = 4 conformal superalgebra and classify the twisted loop conformal superalgebras based on the large N = 4 conformal superalgebra. By considering the corresponding superconformal…