A free resolution for certain algebras

• Grant number: 18/05091-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2018
• End date: August 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Angelo Calil Bianchi
• Grantee: Hilário Fernandes de Araujo Júnior
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil
• Associated research grant: 14/09310-5 - Algebraic structures and their representations, AP.TEM
• Associated scholarship(s): 19/19671-9 - A geometric characterization of the representation type of a quiver, BE.EP.MS

Abstract

The concept of resolution in homological algebra is generally used to define invariants that characterize the structure of a module or objects in a specific category. The goal of this project is to study a free resolution obtained by David Anick for associative algebras. This free resolution is naturally suitable for determining the homology of an algebra. Such construction of resolution was also considered by Kenneth Brown under a method that may possibly be used in different algebraic structures. We intend to specialize the result of Anick to the context of the universal enveloping algebra of certain Kac-Moody algebras and, possibly, certain modules, relying on Brown's ideas. (AU)