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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 theoretic definition.".
- Graded_Lie_algebra wikiPageID "5475402".
- Graded_Lie_algebra wikiPageLength "8827".
- Graded_Lie_algebra wikiPageOutDegree "44".
- Graded_Lie_algebra wikiPageRevisionID "675903075".
- Graded_Lie_algebra wikiPageWikiLink Adjoint_representation_of_a_Lie_algebra.
- Graded_Lie_algebra wikiPageWikiLink Anticommutative.
- Graded_Lie_algebra wikiPageWikiLink Anticommutativity.
- Graded_Lie_algebra wikiPageWikiLink Bilinear_form.
- Graded_Lie_algebra wikiPageWikiLink Braided_monoidal_category.
- Graded_Lie_algebra wikiPageWikiLink Cartan_decomposition.
- Graded_Lie_algebra wikiPageWikiLink Category:Lie_algebras.
- Graded_Lie_algebra wikiPageWikiLink Central_series.
- Graded_Lie_algebra wikiPageWikiLink Characteristic_(algebra).
- Graded_Lie_algebra wikiPageWikiLink Characteristic_of_a_field.
- Graded_Lie_algebra wikiPageWikiLink Commutative_monoid.
- Graded_Lie_algebra wikiPageWikiLink Commutator.
- Graded_Lie_algebra wikiPageWikiLink Connection_(mathematics).
- Graded_Lie_algebra wikiPageWikiLink Coproduct.
- Graded_Lie_algebra wikiPageWikiLink D._C._Spencer.
- Graded_Lie_algebra wikiPageWikiLink Deformation_theory.
- Graded_Lie_algebra wikiPageWikiLink Derivation_(abstract_algebra).
- Graded_Lie_algebra wikiPageWikiLink Derivation_(differential_algebra).
- Graded_Lie_algebra wikiPageWikiLink Differential_geometry.
- Graded_Lie_algebra wikiPageWikiLink Differential_graded_Lie_algebra.
- Graded_Lie_algebra wikiPageWikiLink Donald_C._Spencer.
- Graded_Lie_algebra wikiPageWikiLink Free_Lie_algebra.
- Graded_Lie_algebra wikiPageWikiLink Free_group.
- Graded_Lie_algebra wikiPageWikiLink Frölicher-Nijenhuis_bracket.
- Graded_Lie_algebra wikiPageWikiLink Frölicher–Nijenhuis_bracket.
- Graded_Lie_algebra wikiPageWikiLink Graded_(mathematics).
- Graded_Lie_algebra wikiPageWikiLink Graded_algebra.
- Graded_Lie_algebra wikiPageWikiLink Graded_ring.
- Graded_Lie_algebra wikiPageWikiLink Graded_vector_space.
- Graded_Lie_algebra wikiPageWikiLink Homogeneous_element.
- Graded_Lie_algebra wikiPageWikiLink Homomorphism.
- Graded_Lie_algebra wikiPageWikiLink Kunihiko_Kodaira.
- Graded_Lie_algebra wikiPageWikiLink Lie_algebra.
- Graded_Lie_algebra wikiPageWikiLink Lie_algebra-valued_differential_form.
- Graded_Lie_algebra wikiPageWikiLink Lie_algebra-valued_form.
- Graded_Lie_algebra wikiPageWikiLink Lie_derivative.
- Graded_Lie_algebra wikiPageWikiLink Lie_superalgebra.
- Graded_Lie_algebra wikiPageWikiLink Lower_central_series.
- Graded_Lie_algebra wikiPageWikiLink Mathematics.
- Graded_Lie_algebra wikiPageWikiLink Matrix_(mathematics).
- Graded_Lie_algebra wikiPageWikiLink Monoid.
- Graded_Lie_algebra wikiPageWikiLink Murray_Gerstenhaber.
- Graded_Lie_algebra wikiPageWikiLink Nijenhuis-Richardson_bracket.
- Graded_Lie_algebra wikiPageWikiLink Nijenhuis–Richardson_bracket.
- Graded_Lie_algebra wikiPageWikiLink Parabolic_Lie_algebra.
- Graded_Lie_algebra wikiPageWikiLink Semiring.
- Graded_Lie_algebra wikiPageWikiLink Semisimple_Lie_algebra.
- Graded_Lie_algebra wikiPageWikiLink Superalgebra.
- Graded_Lie_algebra wikiPageWikiLink Supersymmetry.
- Graded_Lie_algebra wikiPageWikiLink Trace-free.
- Graded_Lie_algebra wikiPageWikiLink Trace_(linear_algebra).
- Graded_Lie_algebra wikiPageWikiLink Universal_enveloping_algebra.
- Graded_Lie_algebra wikiPageWikiLinkText "Graded Lie algebra".
- Graded_Lie_algebra wikiPageWikiLinkText "Graded Lie algebra#Supergraded Lie superalgebra".
- Graded_Lie_algebra wikiPageWikiLinkText "graded Jacobi identity".
- Graded_Lie_algebra wikiPageWikiLinkText "graded Lie algebra".
- Graded_Lie_algebra wikiPageWikiLinkText "graded Lie bracket".
- Graded_Lie_algebra wikiPageWikiLinkText "graded Lie superalgebra".
- Graded_Lie_algebra wikiPageWikiLinkText "graded".
- Graded_Lie_algebra wikiPageWikiLinkText "note at graded Lie algebra".
- Graded_Lie_algebra hasPhotoCollection Graded_Lie_algebra.
- Graded_Lie_algebra wikiPageUsesTemplate Template:Main.
- Graded_Lie_algebra subject Category:Lie_algebras.
- Graded_Lie_algebra hypernym Algebra.
- Graded_Lie_algebra type Algebra.
- 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 "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 wasDerivedFrom Graded_Lie_algebra?oldid=675903075.
- Graded_Lie_algebra isPrimaryTopicOf Graded_Lie_algebra.