The Lie algebra sl2=sl2(K) of 2×2 traceless matrices over a field K has only three non-trivial G-gradings when G is a group, the ones induced by G=Z2, Z2×Z2 and Z. Here we prove that when char(K)=0, the variety varG(sl2) of G-graded Lie algebras generated by sl2, is a minimal variety of exponential growth, and in case G=Z2×Z2 or Z, varG(sl2) has almost polynomial growth. © 2013 Elsevier B.V.
Giambruno, A., Da Silva Souza, M. (2014). Minimal varieties of graded Lie algebras of exponential growth and the special Lie algebra sl2. JOURNAL OF PURE AND APPLIED ALGEBRA, 218(8), 1517-1527 [10.1016/j.jpaa.2013.12.003].
Minimal varieties of graded Lie algebras of exponential growth and the special Lie algebra sl2
GIAMBRUNO, Antonino;
2014-01-01
Abstract
The Lie algebra sl2=sl2(K) of 2×2 traceless matrices over a field K has only three non-trivial G-gradings when G is a group, the ones induced by G=Z2, Z2×Z2 and Z. Here we prove that when char(K)=0, the variety varG(sl2) of G-graded Lie algebras generated by sl2, is a minimal variety of exponential growth, and in case G=Z2×Z2 or Z, varG(sl2) has almost polynomial growth. © 2013 Elsevier B.V.
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