A relative theory of universal central extensions

• Author(s): Casas, José Manuel ; Linden, Tim Van der
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/11178
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Categorical Galois theory; Semi-abelian category; Homology; Perfect object; Commutator; Baer invariant; Birkhoff subcategory
• Document Type: Preprint
• Language: English

Description

Basing ourselves on Janelidze and Kelly’s general notion of central extension, we study universal central extensions in the context of semi-abelian categories. Thus we unify classical, recent and new results in one conceptual framework. The theory we develop is relative with respect to a chosen Birkhoff subcategory of the category considered: for instance, we consider groups vs. abelian groups, Lie algebras vs. vector spaces, precrossed modules vs. crossed modules and Leibniz algebras vs. Lie algebras. We also examine the interplay between the relative case and the “absolute” theory determined by the Birkhoff subcategory of all abelian objects. Ministerio de Educacion y Ciencia under grant number MTM2006-15338-C02-02 (includes European FEDER support), by project Ingenio Mathematica (i-MATH) under grant number CSD2006-00032 (Consolider Ingenio 2010); Xunta de Galicia under grant number PGIDITI06PXIB371128PR; CMUC; FCT