Valery Gritsenko (Lille):
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Lorentzian Kac-Moody algebras with 2-reflective Weyl groups

In this talk I present some new results which we obtained recently
with V. Nikulin (see arXiv:1602.08359).
We describe a new large class of Lorentzian Kac-Moody algebras.
For all ranks, we classify 2-reflective hyperbolic lattices S with the
group of 2-reflections of finite volume and with a lattice Weyl
vector. They define the corresponding hyperbolic Kac-Moody algebras
which are graded by S. We construct Lorentzian Kac-Moody algebras
which give their automorphic corrections: they are graded by the S,
have the same simple real roots, but their denominator identities are
given by automorphic forms with 2-reflective divisors. We give exact
constructions of these automorphic forms for most of the lattices
as Borcherds products and, in some cases, as additive Jacobi liftings.