Cohomology ring of n-Lie algebras

• Autores: Mikolaj Rotkiewicz
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 20, Nº 3, 2005, págs. 219-232
• Idioma: inglés
• Títulos paralelos:
  • Anillo de cohomología de n-álgebras de Lie
• Enlaces
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• Resumen

  • Natural graded Lie brackets on the space of cochains of n-Leibniz and n-Lie algebras are introduced. It turns out that these brackets agree under the natural embedding introduced by Gautheron. Moreover, n-Leibniz and n-Lie algebras turn to be canonical structures for these brackets in a similar way in which associative algebras (respectively, Lie algebras) are canonical structures for the Gerstenhaber bracket (respectively, Nijenhuis-Richardson bracket). This allows to define the corresponding cohomology operators and graded Lie algebra structures on the cohomology spaces in an uniform simple way by means of square zero elements.