Related papers: Twisting the fake monster superalgebra
We construct 2 families of automorphic forms related to twisted fake monster algebras and calculate their Fourier expansions. This gives a new proof of their denominator identities and shows that they define automorphic forms of singular…
We show that the physical states of a 10 dimensional superstring moving on a torus form a generalized Kac-Moody superalgebra. This gives the first explicit realizations of these algebras. For a special torus the denominator function of this…
The study of denominator identities for Lie superalgebras was recently developed by M. Gorelik, V.G. Kac, P.Moseneder Frajria, I. Musson, P. Papi, M. Wakimoto and the author. In this paper we generalize these identities to the twisted…
In this paper we consider several problems in the theory of automorphic products and generalized Kac--Moody algebras proposed by Borcherds in 1995. We show that the denominator of the fake monster algebra defines the unique holomorphic…
In the past two decades there has been a great attention to Lie (super)algebras which are extensions of affine Kac-Moody Lie (super)algebras, in certain typical or axiomatic approaches. These Lie (super)algebras have been mostly studied…
We introduce a new, Kac--Moody-flavoured construction for Lie superalgebras, which incorporates phenomena of the type Q (queer) Lie superalgebra. This is done by replacing a maximal even torus by the most general possible Cartan subalgebra…
In the paper we introduce the notion of twisted derivation of a bialgebra. Twisted derivations appear as infinitesimal symmetries of the category of representations. More precisely they are infinitesimal versions of twisted automorphisms of…
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
Using the twisted denominator identity, we derive a closed form root multiplicity formula for all symmetrizable Borcherds-Bozec algebras and discuss its applications including the case of Monster Borcherds-Bozec algebra. In the second half…
We use a Z_2-orbifold of the vertex operator algebra associated to the Niemeier lattice with root lattice A_3^8 and the no-ghost theorem of string theory to construct a generalized Kac-Moody algebra. Borcherds' theory of automorphic…
Starting from Borcherds' fake monster Lie algebra we construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose…
In this paper we study twisted algebras of multiplier Hopf ($^*$-)algebras which generalize all kinds of smash products such as generalized smash products, twisted smash products, diagonal crossed products, L-R-smash products, two-sided…
We extend Norton-Borcherds-Koike's replication formulae to super-replicable ones by working with the congruence groups $\Gamma_1(N)$ and find the product identities which characterize super-replicable functions. These will provide a clue…
We prove denominator identities for the periplectic Lie superalgebra $\mathfrak{p}(n)$, thereby completing the problem of finding denominator identities for all simple classical finite-dimensional Lie superalgebras.
We establish the correspondence between, on one side, the possible gaugings and massive deformations of half-maximal supergravity coupled to vector multiplets and, on the other side, certain generators of the associated very extended…
A lot of developments made during the last years show that Kac-Moody algebras play an important role in the algebraic structure of some supergravity theories. These algebras would generate infinite-dimensional symmetry groups. The possible…
Twisted Calabi-Yau algebras are a generalisation of Ginzburg's notion of Calabi-Yau algebras. Such algebras A come equipped with a modular automorphism \sigma \in Aut(A), the case \sigma = id being precisely the original class of Calabi-Yau…
In this article, we introduce mock-Lie superalgebras, we give some definitions, properties, constructions, and we study their representations. Moreover we introduce pseudo-euclidean mock-Lie superalgebras which are mock-Lie superalgebras…
A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is…
We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.