相关论文: A note on the "logarithmic-W_3" octuplet algebra a…
The w*-closed triple semigroup algebra was introduced by Power and the author in [19], where it was proved to be reflexive and to be chiral, in the sense of not being unitarily equivalent to its adjoint algebra. Here an analogous operator…
The paper purposes to contribute to the classification of pointed Hopf algebras by the method of Andruskiewitsch and Schneider. The structure of arithmetic root systems is enlightened such that their relation to ordinary root systems…
We analyse the SU(2)_k WZNW models beyond the integrable representations and in particular the case of SU(2)_0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally…
We give an explicit presentation of a family of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero that constitute all liftings of Nichols algebras of diagonal Cartan type $B_{3}$ over a…
We propose mixed boundary conditions for 3d conformal gravity consistent with variational principle in its second-order formalism that admit the chiral $\Lambda$-$\mathfrak{bms}_4$ algebra as their asymptotic symmetry algebra. This algebra…
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product…
We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the…
We review various aspects of two dimensional conformal field theories paying close attention to the algebraic structures that intervene. We provide a compact description regarding the appearance of a chiral algebra as the symmetry algebra…
We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra…
We determine all Nichols algebras of finite-dimensional Yetter-Drinfeld modules over groups such that all its left coideal subalgebras in the category of $\mathbb{N}_0$-graded comodules over the group algebra are generated in degree one as…
In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2,2p-1,2p-1,2p-1) series of triplet…
These are lecture notes for an introductory course on Nichols algebras. As a main reference, I work with the book by Heckenberger and Schneider, but I want to take a distinct categorical perspective and try to develop the topic for an…
Over fields of arbitrary characteristic we classify all rank three Nichols algebras of diagonal type with a finite root system. Our proof uses the classification of the finite Weyl groupoids of rank three.
We consider a family of $\mathcal{N}=2$ superconformal field theories in four dimensions, defined as $\mathbb{Z}_q$ orbifolds of $\mathcal{N}=4$ Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a…
For every $p \geq 2$, we obtained an explicit construction of a family of $\mathcal{W}(2,2p-1)$-modules, which decompose as direct sum of simple Virasoro algebra modules. Furthermore, we classified all irreducible self-dual…
We introduce the notion of an asymptotic algebra of chiral differential operators. We then construct, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone.…
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…
It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T_n theories. The…
In two-dimensional conformal field theory (CFT) the building blocks are given by chiral CFTs, i.e.~CFTs on the unit circle (compactified light-ray). They are generated by quantum fields depending on one light-ray coordinate only. There are…