Lie Nilpotency Indices of Restricted Universal Enveloping Algebras

ABSTRACT

For a restricted Lie algebra L over a field of characteristic p > 0 we study the Lie nilpotency index t _L (u(L)) of its restricted universal enveloping algebra u(L). In particular, we determine an upper and a lower bound for t _L (u(L)). Finally, under the assumption that L is p-nilpotent and finite-dimensional, we establish when the Lie nilpotency index of u(L) is maximal.

Communicated by I. Shestakov.

Keywords:

• Lie nilpotency index
• Restricted universal enveloping algebra
• Upper Lie nilpotency index

Mathematics Subject Classification:

• 16S30
• 17B35

ACKNOWLEDGMENT

Salvatore Siciliano and Ernesto Spinelli were partially supported by the National Research Project “Group Theory and Application”.