相关论文: Hyperbolic Kac-Moody superalgebras

A Kac-Moody algebra is called hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. We study root subsystems of root systems of hyperbolic algebras. In this paper, we classify maximal rank regular hyperbolic…

The hyperbolic (and more generally, Lorentzian) Kac-Moody (KM) Lie algebras $\cA$ of rank $r+2 > 2$ are shown to have a rich structure of indefinite KM subalgebras which can be described by specifying a subset of positive real roots of…

We investigate regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras via their Weyl groups. We classify all subgroups relations between Weyl groups of hyperbolic Kac-Moody algebras, and show that for every pair of a group and…

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…

Sometimes a hyperbolic Kac-Moody algebra admits an automorphic correction, meaning a generalized Kac-Moody algebra with the same real simple roots and whose denominator function has good automorphic properties; these for example allow one…

We discuss the known results and methods for determining root multiplicities for hyperbolic Kac--Moody algebras.

We classify regular subalgebras of affine Kac-Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of…

We discuss a general theory of Lorentzian Kac--Moody algebras which should be a hyperbolic analogy of the classical theories of finite-dimensional semi-simple and affine Kac-Moody algebras. First examples of Lorentzian Kac-Moody algebras…

In this paper, we study a special class of indefinite Kac-Moody algebras. Based on the study of hyperbolic Kac-Moody algebras, we give the definition of $N_k$ type Kac-Moody algebras and study some properties of this special type Kac-Moody…

We propose a novel way to define imaginary root subgroups associated with (timelike) imaginary roots of hyperbolic Kac-Moody algebras. Using in an essential way the theory of unitary irreducible representation of covers of the group…

In this paper we study rank two symmetric hyperbolic Kac-Moody algebras H(a) and their automorphic correction in terms of Hilbert modular forms. We associate a family of H(a)'s to the quadratic field Q(p) for each odd prime p and show that…

There exist principal $\mathfrak{sl}_2$ subalgebras for hyperbolic Kac-Moody Lie algebras. In the case of rank 2 symmetric hyperbolic Kac-Moody Lie algebras, certain $\mathfrak{sl}_2$ subalgebras are constructed. These subalgebras are…

In this paper we study root multiplicities of rank 2 hyperbolic Kac-Moody algebras using the combinatorics of Dyck paths.

A subclass of recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes…

The analog of the principal SO(3) subalgebra of a finite dimensional simple Lie algebra can be defined for any hyperbolic Kac Moody algebra g(A) associated with a symmetrizable Cartan matrix A, and coincides with the non-compact group…

Using the coset construction, we compute the root multiplicities at level three for some hyperbolic Kac-Moody algebras including the basic hyperbolic extension of $A_1^{(1)}$ and $E_{10}$.

We consider a natural generalisation of the class of hyperbolic Kac-Moody algebras. We describe in detail the conditions under which these algebras are Lorentzian. We also construct their fundamental weights, and analyse whether they…

In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family…

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for…

In 1983, Feingold and Frenkel discovered a relation between Siegel modular forms of genus two and a rank-three hyperbolic Kac--Moody algebra extending the affine Lie algebra of type $A_1$. It inspires a problem to explore more general…