Research on Hecke-Grothendieck polynomials, metabelian Novikov algebras, Generic Poisson algebras and Novikov-Poisson algebras

• Grant number: 19/02095-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: July 01, 2019
• End date: June 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Zerui Zhang
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The aim of this project is to do research on Hecke-Grothendieck polynomials, metabelian Novikov algebras, Generic Poisson algebras and Novikov-Poisson algebras. More precisely, we shall show that the Hecke-Grothendieck polynomials have nonnegative coefficients under certain assumptions; every finitely generated metabelian Novikov algebra has solvable word problem; we shall establish Composition-Diamond lemma for generic Poisson algebra, to investigate the word problem for one relator generic Poisson algebra and investigate whether the Freiheitssatz holds for Novikov-Poisson algebras.

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

SHESTAKOV, IVAN; ZHANG, ZERUI. Solvability and nilpotency of Novikov algebras. COMMUNICATIONS IN ALGEBRA, v. 48, n. 12, p. 9-pg., 2020-07-08. (19/02095-5, 18/23690-6)

SHESTAKOV, IVAN; ZHANG, ZERUI. Solvability and nilpotency of Novikov algebras. COMMUNICATIONS IN ALGEBRA, JUL 2020. (19/02095-5, 18/23690-6)

SHESTAKOV, IVAN; ZHANG, ZERUI. Automorphisms of finitely generated relatively free bicommutative algebras. Journal of Pure and Applied Algebra, v. 225, n. 8, AUG 2021. (19/02095-5, 18/23690-6)