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<title>GAP (HAP) - Chapter 5: Chain complexes</title>
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<div class="ChapSects"><a href="chap5.html#X7A06103979B92808">5. <span class="Heading"> Chain complexes</span></a>
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<h3>5. <span class="Heading"> Chain complexes</span></h3>
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<td class="tdleft"><code class="code"> ChevalleyEilenbergComplex(X,n) </code></p>
<p>Inputs either a Lie algebra X=A (over the ring of integers Z or over a field K) or a homomorphism of Lie algebras X=(f:A --> B), together with a positive integer n. It returns either the first n terms of the Chevalley-Eilenberg chain complex C(A), or the induced map of Chevalley-Eilenberg complexes C(f):C(A) --> C(B).</p>
<p>(The homology of the Chevalley-Eilenberg complex C(A) is by definition the homology of the Lie algebra A with trivial coefficients in Z or K).</p>
<p>This function was written by Pablo Fernandez Ascariz</td>
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<td class="tdleft"><code class="code"> LeibnizComplex(X,n) </code></p>
<p>Inputs either a Lie or Leibniz algebra X=A (over the ring of integers Z or over a field K) or a homomorphism of Lie or Leibniz algebras X=(f:A --> B), together with a positive integer n. It returns either the first n terms of the Leibniz chain complex C(A), or the induced map of Leibniz complexes C(f):C(A) --> C(B).</p>
<p>(The Leibniz complex C(A) was defined by J.-L.Loday. Its homology is by definition the Leibniz homology of the algebra A).</p>
<p>This function was written by Pablo Fernandez Ascariz</td>
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