Description of root systems with given Weyl group
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The paper is devoted to the description of generalized root systems with a given Weyl group. This problem arises in connection with the classification of infinite-dimensional Lie algebras and in the study of discrete groups generated by reflections. A criterion for the existence of a root system for a given discrete group generated by reflections and an algorithm of describing all root systems with a given Weyl group are obtained.
Key wordsgeneralized root system Weyl group group generated by reflections Lie algebra Cartan subalgebra generalized Cartan matrix Kac-Moody algebra
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- 1.V. G. Kac,Infinite Dimensional Lie Algebras, 3rd edition, Cambridge University Press, Cambridge (1993).Google Scholar