相关论文: $W_{\infty}$ algebra in the integer quantum Hall e…

The BMS symmetry and related near horizon symmetry play important roles in holography in asymptotically flat spacetimes. They may also be crucial for solving the information paradox. But we still don't fully understand those…

It is well known that the centerless W_{1+\infty} algebra provides a hamiltonian structure for the KP hierarchy. In this letter we address the question whether the centerful version plays a similar r\^ole in any related integrable system.…

We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness…

In the previous paper (arXiv:1804.09438) we found that the near horizon symmetry algebra of black holes is a subalgebra of the $W_{1+\infty}$ symmetry algebra of quantum Hall fluid in three dimensional spacetime. In this paper, we give a…

The unitary implementation of a symmetry group $G$ of a classical system in the corresponding quantum theory entails unavoidable deformations $\TG$ of $G$, namely, central extensions by the typical phase invariance group U(1). The…

The problem is the classification of the ideals of ``free differential algebras", or the associated quotient algebras, the q-algebras; being finitely generated, unital C-algebras with homogeneous relations and a q-differential structure.…

We prove the bulk-edge correspondence in $K$-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk…

We construct a quadratic basis of generators of matrix-extended $\mathcal{W}_{1+\infty}$ using a generalization of the Miura transformation. This makes it possible to conjecture a closed-form formula for the operator product expansions…

We review our recent work on the algebraic characterization of quantum Hall fluids. Specifically, we explain how the incompressible quantum fluid ground states can be classified by effective edge field theories with the W-infinity dynamical…

We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral…

We derive the canonical structure and hamiltonian for arbitrary deformations of a higher-dimensional (quantum Hall) droplet of fermions with spin or color on a general phase space manifold. Gauge fields are introduced via a Kaluza-Klein…

In two dimensional fluid, there are only two classes of swimming ways of micro-organisms, {\it i.e.}, ciliated and flagellated motions. Towards understanding of this fact, we analyze the swimming problem by using $w_{1+\infty}$ and/or…

Some algebraic issues of the FQHE are presented. First, it is shown that on the space of Laughlin wavefunctions describing the $\nu =1/m$ FQHE, there is an underlying $W_{\infty}$ algebra, which plays the role of a spectrum generating…

Recent work has revealed intriguing connections between a Belinsky-Khalatnikov-Lifshitz-type analysis of spacelike singularities in General Relativity and certain infinite dimensional Lie algebras, and in particular the `maximally extended'…

We show that the vertex algebra W{1+ \infty} with central charge -1 is isomorphic to a tensor product of the simple W_3 algebra with central charge -2 and a Heisenberg vertex algebra generated by a free bosonic field. We construct a family…

The Lie algebra $\mathcal{D}$ of regular differential operators on the circle has a universal central extension $\hat{\mathcal{D}}$. The invariant subalgebra $\hat{\mathcal{D}}^+$ under an involution preserving the principal gradation was…

We show that the theory of gravity constructed from the non-linear realisation of the semi-direct product of the Kac-Moody algebra A1+++ with its vector representation does not allow a cosmological constant. The existence of a cosmological…

It was demonstrated recently that the $W_{1+\infty}$ algebra contains commutative subalgebras associated with all integer slope rays (including the vertical one). In this paper, we realize that every element of such a ray is associated with…

Over-extended Kac-Moody algebras contain so-called gradient structures - a gl(d)-covariant level decomposition of the algebra contains strings of modules at different levels that can be interpreted as spatial gradients. We present an…

The infinite affine Lie algebras of type ABCD, also called $\widehat{\mathfrak{gl}}(\infty)$, $\widehat{\mathfrak{o}}(\infty)$, $\widehat{\mathfrak{sp}}(\infty)$, are equivalent to subalgebras of the quantum $W_{1+\infty}$ algebras. They…