Hopf algebras in non-associative Lie theory

• Grant number: 12/21938-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 10, 2013
• End date: April 09, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Ivan Chestakov
• Visiting researcher: Jacob Mostovoy
• Visiting researcher institution: Instituto Politécnico Nacional (IPN), Mexico
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 10/50347-9 - Algebras, representations e applications, AP.TEM

Abstract

The objective of the project is to study the universal enveloping algebras of Sabinin algebras in the framework of non-associative Hopf algebras theory. More exactly, we plan to investigate the relation between the universal enveloping algebra U(V) of a Sabinin algebra V and certain associative Hopf algebras; we plan to investigate also whether there exists a reasonable cohomology theory for Sabinin algebras and for non-associative Hopf algebras; finally, we plan to search and describe various invariant subspaces in the universal enveloping algebra of a Sabinin algebra. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MOSTOVOY, J.; PEREZ-IZQUIERDO, J. M.; SHESTAKOV, I. P.. Hopf algebras in non-associative Lie theory. BULLETIN OF MATHEMATICAL SCIENCES, v. 4, n. 1, p. 129-173, APR 2014. (10/50347-9, 12/22537-3, 12/21938-4)

MOSTOVOY, J.; PEREZ-IZQUIERDO, J. M.; SHESTAKOV, I. P.. Nilpotent Sabinin algebras. Journal of Algebra, v. 419, p. 95-123, DEC 1 2014. (10/50347-9, 12/22537-3, 12/21938-4)