Ext groups in the category of bimodules over a simple Leibniz algebra期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Ext groups in the category of bimodules over a simple Leibniz algebra

Authors:	Jean Mugniery Friedrich Wagemann

Affiliation:	1. Laboratoire de Mathématiques, Université Louvain-la-Neuve, Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgique;2. Laboratoire de mathématiques Jean Leray, UMR 6629 du CNRS, Université de Nantes, 2, rue de la Houssinière, F-44322 Nantes Cedex 3, France;1. Departamento de Matematicas, Centro Universitario de Ciencias Exactas e Ingenierias, Universidad de Guadalajara, Mexico;2. School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK;3. Heilbronn Institute for Mathematical Research, Bristol, UK;1. University of Virginia, United States of America;2. Bucknell University, United States of America;1. Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell''Insubria, Via Valleggio 11, 22100 Como, Italy;2. Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Strasse 4, D-24098 Kiel, Germany;3. Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, C/José Antonio Novais 10, 28040 Madrid, Spain;4. Institut für Differentialgeometrie, Gottfried Wilhelm Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany

Abstract:	In this article, we generalize Loday and Pirashvili's [11] computation of the Ext-category of Leibniz bimodules for a simple Lie algebra to the case of a simple (non Lie) Leibniz algebra. Most of the arguments generalize easily, while the main new ingredient is the Feldvoss-Wagemann's cohomology vanishing theorem for semi-simple Leibniz algebras.

Keywords:	Leibniz cohomology Chevalley-Eilenberg cohomology Change of rings spectral sequence Cohomology vanishing Semi-simple Leibniz algebra Ext category of Leibniz bimodules
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