Integrality of exponents of some abelian-by-nilpotent varieties of lie algebras

Abstract

Following I. Volichenko we study varieties of Lie algebras over a field of characteristic zero, satisfying the identity [[x ₁,x ₂,x ₃], [x ₄ x ₅ x ₆]] = 0. We prove that the exponential growth of any proper subvariety is a positive integer and any positive integer can be so realized.

¹⁾Work Partially supported by RFFI Grant Nos. 96-0-00146 and 98-01-01020

²⁾Work Partially supported by ISF grant 6629/1

³⁾Work Partially supported by RFFI Grant Nos. 96-01-00146 and 96-15-96050

¹⁾Work Partially supported by RFFI Grant Nos. 96-0-00146 and 98-01-01020

²⁾Work Partially supported by ISF grant 6629/1

³⁾Work Partially supported by RFFI Grant Nos. 96-01-00146 and 96-15-96050

Notes

¹⁾Work Partially supported by RFFI Grant Nos. 96-0-00146 and 98-01-01020

²⁾Work Partially supported by ISF grant 6629/1

³⁾Work Partially supported by RFFI Grant Nos. 96-01-00146 and 96-15-96050