Han's conjecture

• Grant number: 18/07038-7
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: May 23, 2018
• End date: May 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Eduardo do Nascimento Marcos
• Grantee: Eduardo do Nascimento Marcos
• Visiting researcher: Marcelo Lanzilotta
• Visiting researcher institution: Universidad de la República (UDELAR), Uruguay
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 14/09310-5 - Algebraic structures and their representations, AP.TEM

Abstract

Han's Conjecture. Han's conjecture states that if the number of non zero Hochschild homology groups of an Artin algebra is finite then the algebra has finite global dimension. The reciprocal statement is clearly valid. This conjecture made by Han is a substitute for the similar question made by Happel for the Hochschild Homology, which has conter examples given by Buchweitz, Green, Madson and Solberg. We intend in this visit we plan to work in this conjecture, we already have a proof for the monomial case, which we believe can be generalize for the the general case and we believe we can finish in this visit. (AU)