A non-abelian tensor product of Leibniz algebra
Annales de l'institut Fourier (1999)
- Volume: 49, Issue: 4, page 1149-1177
- ISSN: 0373-0956
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topGnedbaye, Allahtan Victor. "A non-abelian tensor product of Leibniz algebra." Annales de l'institut Fourier 49.4 (1999): 1149-1177. <http://eudml.org/doc/75376>.
@article{Gnedbaye1999,
abstract = {Leibniz algebras are a non-commutative version of usual Lie algebras. We introduce a notion of (pre)crossed Leibniz algebra which is a simultaneous generalization of notions of representation and two-sided ideal of a Leibniz algebra. We construct the Leibniz algebra of biderivations on crossed Leibniz algebras and we define a non-abelian tensor product of Leibniz algebras. These two notions are adjoint to each other. A (co)homological characterization of these new algebraic objects enables us to compare the first order Milnor-type Hochschild homology of an associative algebra (non-necessarily commutative) to its classical Hochschild homology.},
author = {Gnedbaye, Allahtan Victor},
journal = {Annales de l'institut Fourier},
keywords = {Milnor-type Hochschild homology; crossed module; Leibniz algebra; non-abelian Leibniz (co)homology; non-abelian tensor product},
language = {eng},
number = {4},
pages = {1149-1177},
publisher = {Association des Annales de l'Institut Fourier},
title = {A non-abelian tensor product of Leibniz algebra},
url = {http://eudml.org/doc/75376},
volume = {49},
year = {1999},
}
TY - JOUR
AU - Gnedbaye, Allahtan Victor
TI - A non-abelian tensor product of Leibniz algebra
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 4
SP - 1149
EP - 1177
AB - Leibniz algebras are a non-commutative version of usual Lie algebras. We introduce a notion of (pre)crossed Leibniz algebra which is a simultaneous generalization of notions of representation and two-sided ideal of a Leibniz algebra. We construct the Leibniz algebra of biderivations on crossed Leibniz algebras and we define a non-abelian tensor product of Leibniz algebras. These two notions are adjoint to each other. A (co)homological characterization of these new algebraic objects enables us to compare the first order Milnor-type Hochschild homology of an associative algebra (non-necessarily commutative) to its classical Hochschild homology.
LA - eng
KW - Milnor-type Hochschild homology; crossed module; Leibniz algebra; non-abelian Leibniz (co)homology; non-abelian tensor product
UR - http://eudml.org/doc/75376
ER -
References
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- [2] Ch. CUVIER, Algèbres de Leibnitz: définitions, propriétés, Ann. Ecole Norm. Sup., (4) 27 (1994), 1-45. Zbl0821.17024
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- [4] A.V. GNEDBAYE, Third homology groups of universal central extensions of a Lie algebra, Afrika Matematika (to appear), Série 3, 10 (1998). Zbl1054.17003
- [5] D. GUIN, Cohomologie des algèbres de Lie croisées et K-théorie de Milnor additive, Ann. Inst. Fourier, Grenoble, 45-1 (1995), 93-118. Zbl0818.17022MR96e:18004
- [6] J.-L. LODAY, Cyclic homology, Grund. math. Wiss., Springer-Verlag, 301, 1992. Zbl0780.18009MR94a:19004
- [7] J.-L. LODAY, Une version non commutative des algèbres de Lie: les algèbres de Leibniz, L'Enseignement Math., 39 (1993), 269-293. Zbl0806.55009MR95a:19004
- [8] J.-L. LODAY & T. PIRASHVILI, Universal enveloping algebras of Leibniz algebras and (co)homology, Math. Annal., 296 (1993), 139-158. Zbl0821.17022MR94j:17003
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