Free Lie algebra information

In mathematics, a free Lie algebra over a field K is a Lie algebra generated by a set X, without any imposed relations other than the defining relations...

mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket, an...

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...

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

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...

and a semisimple algebra over an algebraically closed field. The universal enveloping algebra of a Lie algebra is an associative algebra that can be used...

permutation. The shuffle algebra on a finite set is the graded dual of the universal enveloping algebra of the free Lie algebra on the set. Over the rational...

In mathematics, especially in the area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since...

affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. Given...

matrix Lie algebra, there is a linear group (matrix Lie group) with this algebra as its Lie algebra. On the other hand, Lie groups with isomorphic Lie algebras...

Lie groups, Lie algebras and their representation theory, a Lie algebra extension e is an enlargement of a given Lie algebra g by another Lie algebra...

free object is one of the basic concepts of abstract algebra. Informally, a free object over a set A can be thought of as being a "generic" algebraic...

mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } ‑grading. Lie superalgebras...

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...

necklace). This counting function also describes the dimensions in a free Lie algebra and the number of irreducible polynomials over a finite field. The...

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 free associative algebra on α generators, and the right hand side is the generating function for the universal enveloping algebra of the free Lie algebra...

algebra of quasisymmetric function. Over the rational numbers it is isomorphic as a Hopf algebra to the universal enveloping algebra of the free Lie algebra...

mathematical theories of Lie groups and Lie algebras. For the topics in the representation theory of Lie groups and Lie algebras, see Glossary of representation...

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...

on free Lie algebras. He proved the Shirshov–Witt theorem, which states that any Lie subalgebra of a free Lie algebra is itself a free Lie algebra. Anatoly...

notion of vertex algebra was introduced by Richard Borcherds in 1986, motivated by a construction of an infinite-dimensional Lie algebra due to Igor Frenkel...

Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is...

series of free groups and free Lie algebras. The group (Z,+) of integers is free of rank 1; a generating set is S = {1}. The integers are also a free abelian...

In mathematics, the Lie operad is an operad whose algebras are Lie algebras. The notion (at least one version) was introduced by Ginzburg & Kapranov (1994)...