Introduction 1. The homotopy category of (2,4)-complexes 2. The homotopy category of simply conne... more Introduction 1. The homotopy category of (2,4)-complexes 2. The homotopy category of simply connected 4-manifolds 3. Track categories 4. The splitting of the linear extension TL 5. The category T Gamma and an algebraic model of CW(2,4) 6. Crossed chain complexes and algebraic models of tracks 7. Quadratic chain complexes and algebraic models of tracks 8. On the cohomology of the category nil.
Using higher Leibniz homology, we introduce the notions of k-perfect and strongly perfect Lie alg... more Using higher Leibniz homology, we introduce the notions of k-perfect and strongly perfect Lie algebras and discuss a relationship with semisimple Lie algebras.
Grundlehren der mathematischen Wissenschaften, 1998
The second Hochschild cohomology group of rings (that is algebras over k = Z) classifies the exte... more The second Hochschild cohomology group of rings (that is algebras over k = Z) classifies the extensions of a ring by a bimodule provided that the ex-tensions are split as abelian groups. In order to classify non-split extensions, Mac Lane introduced in the fifties the so-called Mac Lane (co)homology theory, that we denote by HML and which is closely related to the cohomology of the Eilenberg-Mac Lane spaces. Hochschild (co)homology and Mac Lane (co)homology coincide when the ring contains the rational numbers, but they differ in general.
Abstract We compute the center of various categories, including the category of central extension... more Abstract We compute the center of various categories, including the category of central extensions of a given group G. Our results make use of the Baues–Wirsching cohomology of small categories.
Introduction 1. The homotopy category of (2,4)-complexes 2. The homotopy category of simply conne... more Introduction 1. The homotopy category of (2,4)-complexes 2. The homotopy category of simply connected 4-manifolds 3. Track categories 4. The splitting of the linear extension TL 5. The category T Gamma and an algebraic model of CW(2,4) 6. Crossed chain complexes and algebraic models of tracks 7. Quadratic chain complexes and algebraic models of tracks 8. On the cohomology of the category nil.
Using higher Leibniz homology, we introduce the notions of k-perfect and strongly perfect Lie alg... more Using higher Leibniz homology, we introduce the notions of k-perfect and strongly perfect Lie algebras and discuss a relationship with semisimple Lie algebras.
Grundlehren der mathematischen Wissenschaften, 1998
The second Hochschild cohomology group of rings (that is algebras over k = Z) classifies the exte... more The second Hochschild cohomology group of rings (that is algebras over k = Z) classifies the extensions of a ring by a bimodule provided that the ex-tensions are split as abelian groups. In order to classify non-split extensions, Mac Lane introduced in the fifties the so-called Mac Lane (co)homology theory, that we denote by HML and which is closely related to the cohomology of the Eilenberg-Mac Lane spaces. Hochschild (co)homology and Mac Lane (co)homology coincide when the ring contains the rational numbers, but they differ in general.
Abstract We compute the center of various categories, including the category of central extension... more Abstract We compute the center of various categories, including the category of central extensions of a given group G. Our results make use of the Baues–Wirsching cohomology of small categories.
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Papers by Teimuraz Pirashvili