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Communications in Algebra Volume 31, 2003 - Issue 9
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Original Articles

Non-abelian Tensor Product of Leibniz Algebras and an Exact Sequence in Leibniz Homology

J. M. Casas Departamento Matemática Aplicada, Universidad de Vigo, Pontevedra, Spain; Departamento Matemática Aplicada, Universidad de Vigo, E. U. I. T. Forestal, Campus Universitario A Xunqueira, Pontevedra, 36005, SpainCorrespondence[email protected]
&
M. Ladra Departamento de Algebra, Universidad de Santiago, Santiago de Compostela, Spain; Departamento de Algebra, Universidad de Santiago, Santiago de Compostela, 15782, SpainCorrespondence[email protected]
Pages 4639-4646 | Received 01 Apr 2002, Published online: 01 Feb 2007

References

  • Casas , J. M. 1998 . Central extensions of Leibniz algebras . Extracta Mathematicae , 13 : 393 – 397 .
  • Casas , J. M. and Pirashvili , T. 2000 . Ten-term exact sequence of Leibniz homology . J. Algebra , 231 : 258 – 264 .
  • Ellis , G. J. 1987 . Nonabelian exterior products of Lie algebras and an exact sequence in the homology of Lie algebras . J. Pure Appl. Algebra , 46 : 111 – 115 .
  • Ellis , G. J. 1991 . A non-abelian tensor product of Lie algebras . Glasgow Math. J. , 33 : 101 – 120 .
  • Gnedbaye , V. 1999 . A non-abelian tensor product of Leibniz algebras . Ann. Inst. Fourier (Grenoble) , 49 : 1149 – 1177 .
  • Kassel , C. and Loday , J.-L. 1982 . Extensions centrales d'algèbres de Lie . Ann. Inst. Fourier (Grenoble) , 32 : 119 – 142 .
  • Kurdiani , R. and Pirashvili , T. 2002 . A Leibniz algebra structure on the second tensor power . J. Lie Theory , 12 : 583 – 596 .
  • Loday , J.-L. 1992 . Cyclic homology , Grundl. Math. Wiss. Bd. Vol. 301 , Springer .
  • Loday , J.-L. 1993 . Une version non commutative des algèbres de Lie: les algèbres de Leibniz . L'Enseignement Mathématique , 39 : 269 – 292 .
  • Loday , J.-L. and Pirashvili , T. 1993 . Universal enveloping algebras of Leibniz algebras and (co)homology . Math. Ann. , 296 : 139 – 158 .
  • Ntolo , P. 1994 . Homologie de Leibniz d'algèbres de Lie semi-simples . C. R. Acad. Sci. Paris , t. 318 ( Série I ) : 707 – 710 .
  • R.-Grandjeán , A. 1971 . Retículo de ideales de un objeto en una R-categoría . Rev. Math. Hisp. Amer , 32 : 14 – 20 .

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