Related papers: Loop super-Virasoro Lie conformal superalgebra
We study the representation theory of the N=1 super Heisenberg-Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg-Virasoro vertex algebra arXiv:math/0201314, arXiv:1405.1707 and arXiv:1703.00531 to the…
The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field F whose characteristic is not equal to 2 are studied. The irreducible modules of vertex operator algebra…
In this paper, we study a class of non-weight modules over the affine-Virasoro algebra of type $A_1$, which are free modules of rank one when restricted to the Cartan subalgebra (modulo center). We give the classification of such modules.…
We formalize in Lean certain calculational proofs about infinite-dimensional Lie algebras. Specifically, we construct the Virasoro algebra as a central extension of the Witt algebra associated with a nontrivial 2-cocycle, and we construct…
Two classes of irreducible highest weight modules of the general linear Lie superalgebra $gl(1/\infty)$ are constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the algebra…
We develop a calculus of variations for functionals on certain spaces of conformal maps. Such a space \Omega\ is composed of all maps that are conformal on domains containing a fix compact annular set of the Riemann sphere, and that are…
We construct a class of non-weight modules over the twisted $N=2$ superconformal algebra $\T$. Let $\mathfrak{h}=\C L_0\oplus\C G_0$ be the Cartan subalgebra of $\T$, and let $\mathfrak{t}=\C L_0$ be the Cartan subalgebra of even part…
We provide an Operator Algebraic approach to N=2 chiral Conformal Field Theory and set up the Noncommutative Geometric framework. Compared to the N=1 case, the structure here is much richer. There are naturally associated nets of spectral…
We classify all uniserial modules of the solvable Lie algebra $\mathfrak{g}=\langle x\rangle \ltimes V$, where $V$ is an abelian Lie algebra over an algebraically closed field of characteristic 0 and $x$ is an arbitrary automorphism of $V$.
We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…
In this paper, Whittaker modules are studied for a subalgebra $\mathfrak{q}_{\epsilon}$ of the $\emph{N}$=2 superconformal algebra. The Whittaker modules are classified by central characters. Additionally, criteria for the irreducibility of…
In this paper we explore the possibility of endowing simple infinite-dimensional ${\mathfrak{sl}_2(\mathbb{C})}$-modules by the structure of the graded module. The gradings on finite-dimensional simple module over simple Lie algebras has…
We consider all genus two correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of a sequence of…
We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules…
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…
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…
For any $a,b\in\mathbb C$, $W(a,b)$ is the Lie algebra with basis $\{L_m,M_m\,|\,m\in\mathbb Z\}$ and relations $[L_m,L_n]=(n-m)L_{m+n},$ $[L_m,W_n]=(a+n+bm)W_{m+n}$, $[W_m,W_n]=0$ for $m,n\in\mathbb Z$. For any $\lambda\in\mathbb C^*,$…
In this paper, we construct a class of simple weight modules over the twisted Heisenberg-Virasoro algebra and gap-$p$ Virasoro algebras from restricted modules over some positive part subalgebra of the twisted Heisenberg-Virasoro algebra.…
In this paper, we classify the irreducible Harish-Chandra modules over the full toroidal Lie algebra, which is a natural higher-dimensional analogue of the affine-Virasoro algebra. In particular, we complete the classification of…
In this paper, we introduce a family of functors denoted $\mathscr{F}_b$ that act on algebraic D-modules and generate modules over N=2 superconformal algebras. We prove these functors preserve irreducibility for all values of $b$, with a…