Related papers: Linearizing W-Algebras

In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each…

The most disappointing aspect of $\W$-strings is probably the fact that at least for the known models one does not recover a physical spectrum that differs much from that of ordinary string theory. It is hoped that this is not an intrinsic…

A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras. We emphasize various interactions…

In 2D conformal quantum field theory, we continue a systematic study of W-algebras with two and three generators and their highest weight representations focussing mainly on rational models. We review the known facts about rational models…

We consider the extended superconformal algebras of the Knizhnik-Bershadsky type with $W$-algebra like composite operators occurring in the commutation relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2, only. These…

We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3^{(2)}$ algebra (its classical version) in terms of the spin 1 unconstrained supercurrent generating a $N=2$ superconformal subalgebra and the spins 1/2, 2 bosonic…

We consider real forms of Lie algebras and embeddings of sl(2) which are consistent with the construction of integrable models via Hamiltonian reduction. In other words: we examine possible non-standard reality conditions for non-abelian…

To classify the classical field theories with W-symmetry one has to classify the symplectic leaves of the corresponding W-algebra, which are the intersection of the defining constraint and the coadjoint orbit of the affine Lie algebra if…

A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the…

We present a connection between W-algebras and Yangians, in the case of gl(N) algebras, as well as for twisted Yangians and/or super-Yangians. This connection allows to construct an R-matrix for the W-algebras, and to classify their…

We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra)…

The Bershadsky--Polyakov algebras are the subregular quantum hamiltonian reductions of the affine vertex operator algebras associated with $\mathfrak{sl}_3$. In arXiv:2007.00396 [math.QA], we realised these algebras in terms of the regular…

$W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebras are deformations of ${\mathfrak{bms}_3}$ and ${\mathfrak{bms}_4}$ algebra respectively. We present an $\mathcal{N}=2$ supersymmetric extension of $W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebra…

An elementary proof is given for the existence of infinite dimensional abelian subalgebras in quantum W-algebras. In suitable realizations these subalgebras define the conserved charges of various quantum integrable systems. We consider all…

In this paper, three semilinear substructural logics ULw, IULw and HpsUL*w are constructed. Then the completeness of ULw and IULw with respect to classes of finite UL and IUL-algebras, respectively, is proved. Algebraically, non-integral…

In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to…

Revisiting the results by Winternitz [Symmetry in physics, CRM Proc. Lecture Notes 34, American Mathematical Society, Providence, RI, 2004, pp. 215-227], we thoroughly refine his classification of Lie subalgebras of the real order-three…

We show an algebra morphism between Yangians and some finite W-algebras. This correspondence is nicely illustrated in the framework of the Non Linear Schrodinger hierarchy. For such a purpose, we give an explicit realization of the Yangian…

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure.…

A proposal for constructing a universal nonlinear ${\hat W}_{\infty}$ algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of $D=4$ Self Dual…