Related papers: Affine super Yangians and non-rectangular $W$-supe…
One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist of the…
We construct two families of orthogonal polynomials associated with the universal central extensions of the superelliptic Lie algebras. These polynomials satisfy certain fourth order linear differential equations, and one of the families is…
We review the new approach to the theory of nonlinear $W$-algebras which is developed recently and called {\it conformal linearization}. In this approach $W$-algebras are embedded as subalgebras into some {\it linear conformal} algebras…
In this article, we explicitly construct new finite-dimensional, link-indecomposable Nichols algebras with Dynkin diagrams of type An,Cn,Dn,E6,E7,E8,F4 over any group G with commutator subgroup isomorphic to Z_2.The construction is generic…
In this paper, we give defining relations of the affine Lie superalgebras an and defining relations of a super-version of the Drinfeld[D]-Jimbo[J] affine quantized universal enveloping algebras. As a result, we can exactly define the affine…
Boe, Kujawa and Nakano recently investigated relative cohomology for classical Lie superalgebras and developed a theory of support varieties. The dimensions of these support varieties give a geometric interpretation of the combinatorial…
A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by…
Reductive W-algebras which are generated by bosonic fields of spin-1, a single spin-2 field and fermionic fields of spin-3/2 are classified. Three new cases are found: a `symplectic' family of superconformal algebras which are extended by…
We give explicit formulas for the coproducts of modified Drinfeld-Cartan generating series for the Yangian in type $A$ and for the quantum affine algebras in the particular type $A_2$. As an auxiliary result of the latter, we give an…
This short note is an announcement of results. We continue the study of Yangian-type algebras initiated in the paper arXiv:2208.04809. These algebras share a number of properties of the Yangians of type A but are more massive. We refine and…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
We say that an indecomposable Cartan matrix A with entries in the ground field of characteristic 0 is almost affine if the Lie sub(super)algebra determined by it is not finite dimensional or affine but the Lie (super)algebra determined by…
In a recent paper, the authors have shown that the secondary reduction of W-algebras provides a natural framework for the linearization of W-algebras. In particular, it allows in a very simple way the calculation of the linear algebra…
We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.
We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a…
We define the Drinfeld generators for $Y_3^+$, the twisted Yangian associated to the Lie algebra $\mathfrak{so}_3(\mathbb{C})$. This allows us to define shifted twisted Yangians, which are certain subalgebras of $Y_3^+$. We show that there…
Under usual locality assumptions, we classify all non-integrable distributions with simple infinite-dimensional Lie superalgebra of symmetries over $\mathbb{C}$: we single out 15 series (containing 2 analogs of contact series and one family…
We formulate and prove examples of a conjecture which describes the W-algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine…
We consider the quantum vertex algebra associated with the double Yangian in type A as defined by Etingof and Kazhdan. We show that its center is a commutative associative algebra and construct algebraically independent families of…
$q$-Yangians can be viewed both as quantum deformations of the loop algebras of upper triangular Lie algebras and deformations of the Yangian algebras. In this paper, we study the quantum affine algebra as a product of two copies of the…