Some conjectures and results concerning the homology of nilpotent Lie algebras

DOI10.1016/0001-8708(90)90037-NzbMath0716.17018OpenAlexW2150267331WikidataQ123218947 ScholiaQ123218947MaRDI QIDQ752831

Philip J. Hanlon

Publication date: 1990

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(90)90037-n

zbMATH Keywords

algorithmsKoszul complexuniversal enveloping algebraLie algebra homologycomplex Lie algebraeigenvalues of LaplaciansStrong Macdonald conjectures

Mathematics Subject Classification ID

Exceptional (super)algebras (17B25) Homological methods in Lie (super)algebras (17B55) Cohomology of Lie (super)algebras (17B56) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (8)

Representation homology, Lie algebra cohomology and the derived Harish-Chandra homomorphism ⋮ Representation homology of simply connected spaces ⋮ Twisted strong Macdonald theorems and adjoint orbits ⋮ On the homology of \(\operatorname{sl}_{n}(t\mathbb C[t)\) and a theorem of Stembridge.] ⋮ Highest-weight theory for truncated current Lie algebras ⋮ Some remarkable combinatorial matrices ⋮ On the property M conjecture for the Heisenberg Lie algebra ⋮ The Lie algebra of derivations of a current Lie algebra

Cites Work

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• Cyclic homology and the Macdonald conjectures
• Lie algebra homology and the Macdonald-Kac formulas
• Lie algebra cohomology and the generalized Borel-Weil theorem
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• First Layer Formulas for Characters of SL(n, C)
• A Short Proof of MacDonald's Conjecture for the Root Systems of Type A
• Some Conjectures for Root Systems
• Homologie et cohomologie des algèbres de Lie

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