Simplicial Lie algebra

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In algebra, a simplicial Lie algebra is a simplicial object in the category of Lie algebras. In particular, it is a simplicial abelian group, and thus is subject to the Dold–Kan correspondence.

Lie algebra A vector space with an alternating binary operation satisfying the Jacobi identity.

In mathematics, a Lie algebra is a vector space together with a non-associative, alternating bilinear map , called the Lie bracket, satisfying the Jacobi identity.

In mathematics, more precisely, in the theory of simplicial sets, the Dold–Kan correspondence states that there is an equivalence between the category of chain complexes and the category of simplicial abelian groups. Moreover, under the equivalence, the th homology group of a chain complex is the th homotopy group of the corresponding simplicial abelian group, and a chain homotopy corresponds to a simplicial homotopy.

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Simplicial complex

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Abstract simplicial complex

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<i>n</i>-skeleton

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References

Daniel Gray "Dan" Quillen was an American mathematician.

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.