Related papers: Virasoro 3-algebra from scalar densities
Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 --245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this…
A Virasoro central charge can be associated with each Nichols algebra with diagonal braiding in a way that is invariant under the Weyl groupoid action. The central charge takes very suggestive values for some items in Heckenberger's list of…
Ternary algebras, constructed from ternary commutators, or as we call them, ternutators, defined as the alternating sum of products of three operators, have been shown to satisfy cubic identities as necessary conditions for their existence.…
We find that a compatible graded left-symmetric algebra structure on the Witt algebra induces an indecomposable module of the Witt algebra with 1-dimensional weight spaces by its left multiplication operators. From the classification of…
We investigate the super high-order Virasoro 3-algebra. By applying the appropriate scaling limits on the generators, we obtain the super $w_{\infty}$ 3-algebra which satisfies the generalized fundamental identity condition. We also define…
We study when an sl(2)-representation extends to a representation of the Witt and Virasoro algebras. We give a criterion for extendability and apply it to certain classes of weight sl(2)-modules. For all simple weight sl(2)-modules and…
In this paper we consider extensions of the super Virasoro algebra by one and two super primary fields. Using a non-explicitly covariant approach we compute all SW-algebras with one generator of dimension up to 7 in addition to the super…
In the present article we investigate the possibility of combining the usual Grassmann algebras with their ternary Z_3-graded counterpart, thus creating a more general algebra with coexisting quadratic and cubic constitutive relations. We…
In this paper, we study the $U(1)^2$ Kac--Moody algebra and generalize the standard Sugawara construction of the Virasoro algebra to an infinite family of new realizations. In this case, in addition to the standard invariant tensor…
Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field…
Space-time N=2 and N=4 superconformal algebras can be built using world-sheet free fields or, equivalently, free field representations of osp(1|2) and sl(2|1), respectively. A prescription for the calculation of space-time correlators is…
This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello-Gwilliam. We provide a construction of the Virasoro vertex…
We present a new method to find solutions of the Virasoro master equations for any affine Lie algebra $\widehat{g}$. The basic idea is to consider first the simplified case of an In\"on\"u-Wigner contraction $\widehat{g}_c$ of $\widehat{g}$…
In this note we associate to each Frobenius algebra a vertex algebra, the simplest example being the Virasoro vertex algebra. This construction is analogous to the procedure which associates to a Lie algebra with an invariant bilinear form…
By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the $\mathfrak{bms}_{3}$ algebra are obtained from the Virasoro algebra. We extend this result to construct new families of…
The conformal extension of the BMS$_{3}$ algebra is constructed. Apart from an infinite number of 'superdilatations,' in order to incorporate 'superspecial conformal transformations,' the commutator of the latter with supertranslations…
We give an example of a cluster-tilted algebra A with quiver Q, such that the associated cluster algebra has a denominator vector which is not the dimension vector of any indecomposable A-module. This answers a question posed by T.…
We analyse the algebras generated by free component quantum fields together with the susy generators $Q,\bar Q$. Restricting to hermitian fields we first construct the scalar field algebra from which various scalar superfields can be…
We obtain exhaustive classification of inequivalent realizations of the Witt and Virasoro algebras by Lie vector fields of differential operators in the space $\mathbb{R}^3$. Using this classification we describe all inequivalent…
We discuss the linearization of vector-spinor (spin-3/2) nonlinear supersymmetry (vsNLSUSY) transformations for both $N = 1$ and $N$-extended SUSY in flat spacetime based on the commutator algebra by using functionals (composites) of…