homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often...

abstract algebra and topology, a differential graded Lie algebra (or dg Lie algebra, or dgla) is a graded vector space with added Lie algebra and chain...

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...

differential graded Lie algebra. To be a little more specific, the Jacobi identity only holds up to homotopy. Therefore, a differential graded Lie algebra can...

the Lie bracket. For example, a graded Lie algebra is a Lie algebra (or more generally a Lie superalgebra) with a compatible grading. A differential graded...

and the interior product acting on differential forms. Graded derivations of superalgebras (i.e. Z2-graded algebras) are often called superderivations...

derivative gives the exterior algebra of differential forms on a manifold the structure of a differential graded algebra. The exterior derivative commutes...

mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators...

definition of a graded ring; hence, the notion applies to non-associative algebras as well; e.g., one can consider a graded Lie algebra. Generally, the...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

algebra Differential graded algebra Differential graded Lie algebra Exterior algebra F-algebra Filtered algebra Flexible algebra Freudenthal algebra Functional-theoretic...

In differential geometry, a Lie-algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the...

graded Lie algebra (say, graded by Z {\displaystyle \mathbb {Z} } or N {\displaystyle \mathbb {N} } ) that is anticommutative and has a graded Jacobi identity...

infinite-dimensional Lie algebras Free Lie algebra Graded Lie algebra Differential graded Lie algebra Homotopy Lie algebra Malcev Lie algebra Modular Lie algebra Monster...

it lies. CDGA may refer to the category of augmented differential graded commutative algebras. A graded Lie algebra is a Lie algebra that is graded as...

In algebra, a differential graded module, or dg-module, is a Z {\displaystyle \mathbb {Z} } -graded module together with a differential; i.e., a square-zero...

of this differential on an exterior algebra makes sense for any Lie algebra, so it is used to define Lie algebra cohomology for all Lie algebras. More generally...

mathematics and theoretical physics, a superalgebra is a Z2-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition...

category of Lie algebras. That is, it is left adjoint to the forgetful functor. The free Lie algebra on a set X is naturally graded. The 1-graded component...

representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Operator algebras can be used to study...

complex Koszul complex Moore complex Schur complex Differential graded algebra Differential graded Lie algebra Dold–Kan correspondence says there is an equivalence...

In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also...

as the algebra of generalized Poisson brackets defined on differential forms. A Gerstenhaber algebra is a graded-commutative algebra with a Lie bracket...

equivalent to the homotopy category of connected differential graded Lie algebras. (The associated graded Lie algebra ker ⁡ ( d ) / im ⁡ ( d ) {\displaystyle...

filtered algebra is a generalization of the notion of a graded algebra. Examples appear in many branches of mathematics, especially in homological algebra and...

group, and thus is subject to the Dold–Kan correspondence. Differential graded Lie algebra Quillen, Daniel (September 1969). "Rational homotopy theory"...

a Lie algebra, one can also have representations of a Lie superalgebra, called supermultiplets. For each Lie algebra, there exists an associated Lie group...

the algebra of tensor fields of the underlying manifold. The Lie derivative commutes with contraction and the exterior derivative on differential forms...

representation theory, mathematical physics, operator algebras, complex analysis, and the theory of partial differential equations. K-theory is an independent discipline...

of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms...