COMPARISON OF PRODUCTS OF THE VARIETIES OF LIE ALGEBRAS

Abstract

Assume that a product 1…k of some varieties of Lie algebras over an infinite field is a subvariety of another product 1,…,ℓ. What can one say about the factors? We make clear in the paper how all such examples can be constructed.

Keywords:

• Varieties
• Lie algebras
• Polynomial identities
• Free algebras
• Wreath products

ACKNOWLEDGMENTS

Both authors were supported in part by the Russian Fund for Basic Research 99-01-00894, the research of the first author was supported in part by the NSF grant DMS 0072307.