Algebras whose generating ideals have small Groebner basis

• Grant number: 16/19459-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 02, 2017
• End date: March 09, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Eduardo do Nascimento Marcos
• Grantee: Eduardo do Nascimento Marcos
• Visiting researcher: Edward L. Green
• Visiting researcher institution: Virginia Polytechnic Institute and State University, United States
• 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

One of the most important, interesting and sometimes hard to compute when dealing with quotient of Quiver algebras is the computation of a Gröbner basis of the ideal of the algebra. Once this computation is made one can ask which properties of the algebra can be deduced from this. We plan to start the attack in this direction by studing algebras whose ideal have Gröbner basis with small cardinality. Professor Ed. Green is also comming to talk with my PhD student Alex Sierra, who is working in computation of the center of Brouer Configuration algebras, which where introduced by Prof. Green. He is also going to interact with my student Ana Melissa Paiba Amaya who has a master scholarship from FAPESP whose work is based on some of his paper. (AU)