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...

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...

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...

space form a graded Lie algebra, using the Whitehead product. In a related construction, Daniel Quillen used differential graded Lie algebras over the rational...

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

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

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...

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...

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...

any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the...

prove the monstrous moonshine conjectures. The monster Lie algebra is a Z2-graded Lie algebra. The piece of degree (m, n) has dimension cmn if (m, n)...

enveloping algebra Baker-Campbell-Hausdorff formula Casimir invariant Killing form Kac–Moody algebra Affine Lie algebra Loop algebra Graded Lie algebra One-parameter...

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

This still gave rise to a Lie algebra, but one which is now infinite dimensional. Simultaneously, Z-graded Lie algebras were being studied in Moscow...

In mathematics, a generalized Kac–Moody algebra is a Lie algebra that is similar to a Kac–Moody algebra, except that it is allowed to have imaginary simple...

In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. For a Lie algebra g {\displaystyle {\mathfrak...

mathematics, Lie algebra cohomology is a cohomology theory for Lie algebras. It was first introduced in 1929 by Élie Cartan to study the topology of Lie groups...

unital, but Lie algebras never are. The nonassociative algebra structure of A may be studied by associating it with other associative algebras which are...

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

the two algebraic descriptions of the rational homotopy category. In short, a Lie algebra determines a graded-commutative algebra by Lie algebra cohomology...

In mathematics, an anyonic Lie algebra is a U(1) graded vector space L {\displaystyle L} over C {\displaystyle \mathbb {C} } equipped with a bilinear operator...

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...

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

In mathematics, a Malcev Lie algebra, or Mal'tsev Lie algebra, is a generalization of a rational nilpotent Lie algebra, and Malcev groups are similar...

algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. In two dimensions, the superconformal algebra is...

Z2-graded representation of the universal enveloping algebra of L which respects the third equation above. A * Lie superalgebra is a complex Lie superalgebra...

natural Hopf algebra homomorphism U ( P ( A ) ) → A {\displaystyle U(P(A))\to A} from the universal enveloping algebra of the graded Lie algebra P ( A ) {\displaystyle...

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

forms. Graded derivations of superalgebras (i.e. Z2-graded algebras) are often called superderivations. Hasse–Schmidt derivations are K-algebra homomorphisms...

differential graded algebra. A Poisson algebra is a commutative associative algebra over a field together with a structure of a Lie algebra so that the Lie bracket...