Minimal varieties of graded Lie algebras of exponential growth and the special Lie algebra sl(2)

Author(s)

Giambruno, Antonio ^[1] ; Souza, Manuela da Silva ^[2]

Affiliation

^[1] Univ Palermo, Dipartimento Matemat & Informat, I-90123 Palermo - Italy

^[2] Univ Sao Paulo, IME, Dept Matemat, BR-05508090 Sao Paulo - Brazil

• Document type: Journal article
• Source: Journal of Pure and Applied Algebra; v. 218, n. 8, p. 1517-1527, AUG 2014.
• Web of Science Citations: 1

Abstract

The Lie algebra sl(2) = sl(2)(K) of 2 x 2 traceless matrices over a field K has only three nontrivial G-gradings when G is a group, the ones induced by G = Z(2), Z(2) X Z(2) and Z. Here we prove that when char(K) = 0, the variety var(G)(sl(2)) of G-graded Lie algebras generated by sl(2), is a minimal variety of exponential growth, and in case G = Z(2) X Z(2) or Z, varG (sl(2)) has almost polynomial growth. (AU)

• FAPESP's process: 13/04590-7 - Star-group identities and Lie nilpotence
• Grantee: Manuela da Silva Souza
• Support Opportunities: Scholarships in Brazil - Post-Doctoral