Geodesic
Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac--Moody algebras
Izvestiya. Mathematics , Tome 60 (1996) no. 2, pp. 305-334

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We develop a theory of Lorentzian Kac–Moody algebras based on the theory of reflection groups in Lobachevskii spaces and on recent results of R. Borcherds. 
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     author = {V. V. Nikulin},
     title = {Reflection groups in {Lobachevskii} spaces and the denominator identity for {Lorentzian} {Kac--Moody} algebras},
     journal = {Izvestiya. Mathematics },
     pages = {305--334},
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     number = {2},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1996_60_2_a3/}
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V. V. Nikulin. Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac--Moody algebras. Izvestiya. Mathematics , Tome 60 (1996) no. 2, pp. 305-334. http://geodesic.mathdoc.fr/item/IM2_1996_60_2_a3/