Complete Classification of BKM Lie Superalgebras Possessing Special Imaginary Roots

REFERENCES

• Bennett , C. ( 1993 ). Imaginary roots of a Kac–Moody algebra whose reflections preserve root multiplicities . J. Algebra 158 : 244 – 267 .
   Web of Science ®Google Scholar
• Borcherds , R. E. ( 1988 ). Generalized Kac–Moody algebras . J. Algebra 115 : 501 – 512 .
   Web of Science ®Google Scholar
• Casperson , D. ( 1994 ). Strictly imaginary roots of Kac–Moody algebras . J. Algebra 168 : 90 – 122 .
   Web of Science ®Google Scholar
• Jurgen , F. , Urmie , R. , Chritoph , S. ( 1997 ). Some automorphisms of generalized Kac-Moody algebras . J. Algebra 191 : 518 – 540 .
   Web of Science ®Google Scholar
• Kac , V. G. ( 1977 ). Lie superalgebras . Adv. Math. 26 : 8 – 96 .
   Web of Science ®Google Scholar
• Kac , V. G. ( 1978 ). Infinite dimensional algebras, Dedekind's η-function, classical Mobius function and the very strange formula . Adv. Math. 30 : 85 – 136 .
   Web of Science ®Google Scholar
• Kac , V. G. ( 1990 ). Infinite Dimensional Lie Algebras. , 3rd ed. Cambridge : Cambridge University Press .
   Google Scholar
• Li , Z.-H. , Jin , Y.-D. , Bai , R.-P. ( 1999 ). Relationship between reflections determined by imaginary roots and the Weyl group for a special GKM algebra . J. Math. Res. Exp. 19 ( 3 ): 501 – 507 .
   Google Scholar
• Marotta , V. , Sciarrino , A. ( 1995 ). Realization of Borcherds algebras . Int. J. Mod. Phys. A 10 ( 27 ): 3921 – 3936 .
   Web of Science ®Google Scholar
• Miyamoto , M. ( 1996 ). A generalization of Borcherds algebra and denominator formula, the recursive dimension formula . J. Algebra 180 : 631 – 651 .
   Web of Science ®Google Scholar
• Satoshi , N. ( 1995 ). Kazhdan–Lusztig conjecture for generalized Kac–Moody algebras II. Proof of the conjecture . Trans. Amer. Math. Soc. 347 ( 10 ): 3891 – 3919 .
   Web of Science ®Google Scholar
• Sthanumoorthy , N. , Uma Maheswari , A. (1996). Purely imaginary roots of Kac–Moody algebras. Comm. Algebra. 24(2):677–693.
   Web of Science ®Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. ( 2000 ). On the root system of generalized Kac–Moody algebras . J. Madras University (WMY-2000 Special Issue) Section B: Sciences 52 : 81 – 103 .
   Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. ( 2002 ). Special imaginary roots of generalized Kac–Moody algebras . Comm. Algebra 30 ( 10 ): 4771 – 4787 .
   Web of Science ®Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. ( 2003 ). A note on purely imaginary roots of generalized Kac–Moody algebras . Comm. Algebra 31 ( 11 ): 5467 – 5479 .
   Web of Science ®Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. ( 2004 ). On some classess of root systems of generalized Kac–Moody algebras . Contemporary Mathematics, AMS 343 : 289 – 313 .
   Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. ( 2007 ). Complete classifications of generalized Kac–Moody algebras possessing special imaginary roots and strictly imaginary property . Comm. Algebra 35 : 2450 – 2471 .
   Web of Science ®Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. , Nazeer Basha , A. ( 2007 ). Special imaginary roots of BKM Lie superalgebras . Inter. Jour. Pure and applied Maths 38 ( 4 ): 513 – 542 .
   Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. , Nazeer Basha , A. ( 2009 ). Strictly imaginary roots and purely imaginary roots of BKM Lie superalgebras . Comm. Algebra 37 ( 7 ): 2357 – 2390 .
   Web of Science ®Google Scholar
• Ray , U. ( 2007 ). Automorphic Forms and Lie Superalgebras . Dordrecht : Springer .
   Google Scholar
• Wakimoto , M. ( 1999 ). Infinite dimensional Lie algebras, Originally published in Japanese by Iwanami Publishers, Tokyo. Translated from the Japanese by Kenji Iohara .
   Google Scholar
• Communicated by K. Mishra.
   Google Scholar