POLYCYCLIC RESTRICTED LIE ALGEBRAS

Abstract

We define a polycyclic restricted Lie algebra to be the Lie analog of a polycyclic group, and we describe the structure of poly(cyclic or finite-dimensional) restricted Lie algebras. In particular, we prove that these are precisely the restricted Lie algebras whose restricted enveloping algebras have polynomial growth.

^*The first author's research was supported in part by NSF Grant DMS-9820271.

^†The second author's research was partially supported by grants RFBR 98-01-01020 and 99-01-00233.

Keywords:

• 1991 Mathematics Subject Classification: [2000] 16S30, 16P90, 17B35, 17B50

Acknowledgments

Notes

^*The first author's research was supported in part by NSF Grant DMS-9820271.

^†The second author's research was partially supported by grants RFBR 98-01-01020 and 99-01-00233.