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

作者：Giambruno Antonio; Souza Manuela da Silva^*

来源：Journal of Pure and Applied Algebra, 2014, 218(8): 1517-1527.

DOI：10.1016/j.jpaa.2013.12.003

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.

• 出版日期2014-8