A class of Lie algebras arising from intersection matrices

Allison B, Benkart G, Gao Y. Lie Algebras Graded by the Root System BC r, r ⩽ 2. Mem Amer Math Soc, No 751. Providence: Amer Math Soc, 2002 Benkart G, Zelmanov E. Lie algebras graded by finite root systems and intersection matrix algebras. Invent Math, 1996, 126: 1–45 Berman S. On generators and relations for certain involutory subalgebras of Kac-Moody Lie algebras. Comm Algebra, 1989, 17: 3165–3185 Berman S, Jurisich E, Tan S. Beyond Borcherds Lie algebras and inside. Trans Amer Math Soc, 2001, 353: 1183–1219 Berman S, Moody R V. Lie algebras graded by finite root systems and the intersection matrix algebras of Slowdowy. Invent Math, 1992, 108: 323–347 Bhargava S, Gao Y. Realizations of BCr-graded intersection matrix algebras with grading subalgebras of type B r, r ⩽ 3. Pacific J Math, 2013, 263(2): 257–281 Carter R. Lie Algebras of Finite and Affine Type. Cambridge: Cambridge Univ Press, 2005 Eswara Rao S, Moody R V, Yokonuma T. Lie algebras and Weyl groups arising from vertex operator representations. Nova J Algebra and Geometry, 1992, 1: 15–57 Gabber O, Kac V G. On defining relations of certain infinite-dimensional Lie algebras. Bull Amer Math Soc (NS), 1981, 5: 185–189 Gao Y. Involutive Lie algebras graded by finite root systems and compact forms of IM algebras. Math Z, 1996, 223: 651–672 Gao Y, Xia L. Finite-dimensional representations for a class of generalized intersection matrix algebras. arXiv: 1404.4310v1 Humphreys J E. Introduction to Lie Algebras and Representation Theory. New York: Springer, 1972 Jacobson N. Lie Algebras. New York: Inter Science, 1962 Kac V G. Infinite Dimensional Lie Algebras. 3rd ed. Cambridge: Cambridge, Univ Press, 1990 Lusztig G. Introduction to quantum groups. Boston: Birkhäuser, 1993 Neher E. Lie algebras graded by 3-graded root systems and Jordan pairs covered by grids. Amer J Math, 1996, 118(2): 439–491 Peng L. Intersection matrix Lie algebras and Ringel-Hall Lie algebras of tilted algebras. In: Happel D, Zhang Y B, eds. Proc 9-th Inter Conf Representation of Algebras, Vol I. Beijing: Beijing Normal Univ Press, 2002, 98–108 Peng L, Xu M. Symmetrizable intersection matrices and their root systems. arXiv: 0912.1024 Slodowy P. Singularitäten, Kac-Moody Lie-Algebren, assoziierte Gruppen und Verallgemeinerungen. Habilitationsschrift, Universität Bonn, March 1984 Slodowy P. Beyond Kac-Moody algebras and inside. Can Math Soc Conf Proc, 1986, 5: 361–371 Xu M, Peng L. Symmetrizable intersection matrix Lie algebras. Algebra Colloq 2011, 18(4): 639–646