相关论文: Hyperbolic Kac-Moody superalgebras

We prove that in a cocompact complex hyperbolic arithmetic lattice $\Gamma < {\rm PU}(m,1)$ of the simplest type, deep enough finite index subgroups admit plenty of homomorphisms to $\mathbb{Z}$ with kernel of type $\mathscr{F}_{m-1}$ but…

In a recent paper ([1],[2]) we have classified explicitely all the unitary highest weight representations of non compact real forms of semisimple Lie Algebras on Hermitian symmetric space. These results are necessary in order to construct…

The group of automorphisms of the Kac Jordan superalgebra is described, and used to classify the maximal subalgebras.

Varchenko's approach to quantum groups, from the theory of arrangements of hyperplanes, can be usefully applied to q-algebras in general, of which quantum groups and quantum (super) Kac-Moody algebras are special cases. New results are…

$N\leq 8$ 3-algebras have recently appeared in N-supersymmetric 3-dimensional Chern-Simons gauge theories. In our previous paper we classified linearly compact simple N = 8 n-algebras for any $n \geq 3$. In the present paper we classify…

In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi/p with p no smaller than 2. We will mainly concentrate on the groups where some elements are…

Let $\Delta$ be a rank 2 hyperbolic root system. Then $\Delta$ has generalized Cartan matrix $H(a,b)= \left(\begin{smallmatrix} ~2 & -b\\ -a & ~2 \end{smallmatrix}\right)$ indexed by $a,b\in\mathbb{Z}$ with $ab\geq 5$. If $a\neq b$, then…

We consider the relation between higher spin gauge fields and real Kac-Moody Lie algebras. These algebras are obtained by double and triple extensions of real forms g_0 of the finite-dimensional simple algebras g arising in dimensional…

In this paper, we compute basis elements of certain spaces of weight 0 weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the…

We construct families of hyperbolic hypersurfaces of degree $2n$ in the projective space $\mathbb{P}^n(\mathbb{C})$ for $3 \leq n \leq 6$.

In this paper, we compute the rational cohomology groups of the classifying space of a simply connected Kac-Moody group of infinite type. The fundamental principle is "from finite to infinite". That is, for a Kac-Moody group G(A) of…

Using the quaternionic formalism for the description of the group of isometries of hyperbolic $5$-space we consider arithmetically defined $5$-dimensional hyperbolic manifolds which are non-compact but of finite volume. They arise from…

We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal…

We count the number of conjugacy classes of maximal, genus g, surface subroups in hyperbolic 3-manifold groups. For any closed hyperbolic 3-manifold, we show that there is an upper bound on this number which grows factorially with g. We…

We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.

We consider epimorphisms from quantum minimal surface algebras onto involutroy subalgebras of split real simply-laced Kac-Moody algebras and provide examples of affine and finite type. We also provide epimorphisms onto such Kac-Moody…

Using Kirchberg-Phillips' classification of purely infinite C*-algebras by K-theory, we prove that the isomorphism types of crossed product C*-algebras associated to certain hyperbolic 3-manifold groups acting on their Gromov boundary only…

Superderivations for the eight families of finite or infinite dimensional graded Lie superalgebras of Cartan-type over a field of characteristic $p>3$ are completely determined by a uniform approach: The infinite dimensional case is reduced…

This paper contains a purely topological theorem and a geometric application. The topological theorem states that if M is a simple closed orientable 3-manifold such that \pi_1(M) contains a genus g surface group and H_1(M;Z/2Z) has rank at…

Infinite-dimensional Lie superalgebras, particularly Borcherds-Kac-Moody (BKM) superalgebras, play a fundamental role in mathematical physics, number theory, and representation theory. In this paper, we study the root multiplicities of BKM…