. . . . . . . . . . . "In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket operation. A choice of Cartan decomposition endows any semisimple Lie algebra with the structure of a graded Lie algebra. Any parabolic Lie algebra is also a graded Lie algebra."@en . . . . . . . . . . "In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket operation. A choice of Cartan decomposition endows any semisimple Lie algebra with the structure of a graded Lie algebra. Any parabolic Lie algebra is also a graded Lie algebra. A graded Lie superalgebra extends the notion of a graded Lie algebra in such a way that the Lie bracket is no longer assumed to be necessarily anticommutative. These arise in the study of derivations on graded algebras, in the deformation theory of Murray Gerstenhaber, Kunihiko Kodaira, and Donald C. Spencer, and in the theory of Lie derivatives. A supergraded Lie superalgebra is a further generalization of this notion to the category of superalgebras in which a graded Lie superalgebra is endowed with an additional super -gradation. These arise when one forms a graded Lie superalgebra in a classical (non-supersymmetric) setting, and then tensorizes to obtain the supersymmetric analog. Still greater generalizations are possible to Lie algebras over a class of braided monoidal categories equipped with a coproduct and some notion of a gradation compatible with the braiding in the category. For hints in this direction, see Lie superalgebra#Category-theoretic definition."@en . "9570"^^ . . "In matematica, un'algebra di Lie si dice graduata quando \u00E8 dotata di una gradazione compatibile con le parentesi di Lie. In altre parole, essa \u00E8 un'algebra di Lie che \u00E8 un'algebra graduata non-associativa nel quadro dell'operazione di commutazione. Questo concetto viene esteso nella superalgebra di Lie graduata, in cui si richiede che le parentesi di Lie non siano necessariamente anticommutative."@it . . "5475402"^^ . . . . . . . . . . . . "In matematica, un'algebra di Lie si dice graduata quando \u00E8 dotata di una gradazione compatibile con le parentesi di Lie. In altre parole, essa \u00E8 un'algebra di Lie che \u00E8 un'algebra graduata non-associativa nel quadro dell'operazione di commutazione. Questo concetto viene esteso nella superalgebra di Lie graduata, in cui si richiede che le parentesi di Lie non siano necessariamente anticommutative."@it . . . . . . "Graded Lie algebra"@en . . . . . . . "1074866903"^^ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Algebra di Lie graduata"@it . . . .