Strictly Imaginary Roots and Purely Imaginary Roots of BKM Lie Superalgebras

REFERENCES

• Bennett , C. ( 1993 ). Imaginary roots of a Kac–Moody Lie algebra whose reflections preserve root multiplicities . J. Algebra 158 : 244 – 267 .
   Web of Science ®Google Scholar
• Borcherds , R. E. ( 1998 ). 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
• Kac , V. G. ( 1978 ). Infinite dimensional algebras, Dedkind's η-function, classical Möbius 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 : 501 – 507 .
   Google Scholar
• Sthanumoorthy , N. , Uma Maheswari , A. ( 1996 ). Purely imaginary roots of Kac–Moody algebras . Comm. Algebra 24 : 677 – 693 .
   Web of Science ®Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. ( 2000 ). On the root systems 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 : 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 : 5467 – 5480 .
   Web of Science ®Google Scholar
• Sthanumoorthy , N. , Lilly , P. L. ( 2004 ). On some classes of root systems of generalized Kac–Moody algebras . Contemp. Math. 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
• Wakimoto , M. ( 1999 ). Infinite Dimensional Lie Algebras . Originally Published in Japanese . Tokyo : Iwanami Publishers .
   Google Scholar
• Wan , Z. ( 1991 ). Introduction to Kac–Moody Algebras . World Scientific Publ. Co. Ltd .
   Google Scholar
• Communicated by K. C. Misra.
   Google Scholar