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- Graded_Lie_algebra abstract "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 M. Gerstenhaber, Kunihiko Kodaira, and D. 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 Z/2Z-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 algebra#Category theory definition.".
- Graded_Lie_algebra wikiPageID "5475402".
- Graded_Lie_algebra wikiPageRevisionID "593817695".
- Graded_Lie_algebra hasPhotoCollection Graded_Lie_algebra.
- Graded_Lie_algebra subject Category:Lie_algebras.
- Graded_Lie_algebra type Abstraction100002137.
- Graded_Lie_algebra type Algebra106012726.
- Graded_Lie_algebra type Cognition100023271.
- Graded_Lie_algebra type Content105809192.
- Graded_Lie_algebra type Discipline105996646.
- Graded_Lie_algebra type KnowledgeDomain105999266.
- Graded_Lie_algebra type LieAlgebras.
- Graded_Lie_algebra type Mathematics106000644.
- Graded_Lie_algebra type PsychologicalFeature100023100.
- Graded_Lie_algebra type PureMathematics106003682.
- Graded_Lie_algebra type Science105999797.
- Graded_Lie_algebra comment "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.".
- Graded_Lie_algebra label "Algebra di Lie graduata".
- Graded_Lie_algebra label "Graded Lie algebra".
- Graded_Lie_algebra sameAs Algebra_di_Lie_graduata.
- Graded_Lie_algebra sameAs m.0dnhw3.
- Graded_Lie_algebra sameAs Q3611543.
- Graded_Lie_algebra sameAs Q3611543.
- Graded_Lie_algebra sameAs Graded_Lie_algebra.
- Graded_Lie_algebra wasDerivedFrom Graded_Lie_algebra?oldid=593817695.
- Graded_Lie_algebra isPrimaryTopicOf Graded_Lie_algebra.