Quantum calculus and the non-comutative plane

• Grant number: 08/01105-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2008
• End date: May 31, 2009
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Roldão da Rocha
• Grantee: Ana Cláudia Lopes Onório
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

Using fundamental concepts of q-quantum calculus, we investigate the principle of q-counting in combinatorial analysis and partition of the classic integer numbers, in order to introduce matrices on the non-commutative 2-dimensional space. The central objective of this project is first to introduce the fundamentals of the calculus on lattices via q-calculation and subsequent investigate some properties, as the group of matrices on the 2-dimensional space of non-commutative variables. We also investigate the symmetric q-calculus, in an approach that will lead to a definition of the generators of the algebra sl(2) in this context. The implementation of this project introduces the student in the fundamental concepts to further study of various topics, such as non-commutative geometry and quantum groups, in addition to several other applications.