Journal of East China Normal University(Natural Sc ›› 2008, Vol. 2008 ›› Issue (3): 51-58.

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I(x)-Reduced representations of generalized Jacobson-Witt algebras W(m;n)(English)

LI Sha-sha1, SHU Bin2   

  1. 1. School of Mathematics and Information Science, Shandong University of Technology, Zibo Shandong 255049, China 2. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2007-05-23 Revised:2007-10-11 Online:2008-05-25 Published:2008-05-25
  • Contact: SHU Bin

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Abstract: This paper studied the representations of graded Cartan type Lie algebra W(m;n) in characteristic p>2, by generalizing the arguments of Shu's for restricted Lie algebras W(m;1). Especially, the rank-reducing method exploited in the restricted case was extended to non-restricted case. The simple
modules for W(m;n) with generalized p-character x were described by reduction when x was regular semisimple.

Key words: Cartan type, regular semisimple, loop algebra, graded lie algebra, Cartan type, regular semisimple, loop algebra

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