The simple graded lie algebras of characteristic three with classical reductive component L₀

Abstract

We determine all finite-dimensional simple graded Lie algebras over an algebraically closed field of characteristic three with a classical reductive component L ₀ and a nonrestricted representation on L _-1.

¹The first author gratefully acknowledges support from NSF Grant #DMS-9300523.

²The main results of this paper were obtained while the second and third authors vis-ited the University of Wisconsin, Madison under the sponsorship of NSF Grant # DMS-9115984. They would like to thank the University of Wisconsin, Madison for its hospitality and the National Science Foundation for its support. They also gratefully acknowledge partial support from ISF Grant MCN000 and grants from the RFFI.

¹The first author gratefully acknowledges support from NSF Grant #DMS-9300523.

²The main results of this paper were obtained while the second and third authors vis-ited the University of Wisconsin, Madison under the sponsorship of NSF Grant # DMS-9115984. They would like to thank the University of Wisconsin, Madison for its hospitality and the National Science Foundation for its support. They also gratefully acknowledge partial support from ISF Grant MCN000 and grants from the RFFI.

Notes

¹The first author gratefully acknowledges support from NSF Grant #DMS-9300523.

²The main results of this paper were obtained while the second and third authors vis-ited the University of Wisconsin, Madison under the sponsorship of NSF Grant # DMS-9115984. They would like to thank the University of Wisconsin, Madison for its hospitality and the National Science Foundation for its support. They also gratefully acknowledge partial support from ISF Grant MCN000 and grants from the RFFI.