Tiled orders, partial actions and homological aspects

• Grant number: 13/11350-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2015
• End date: March 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Mikhailo Dokuchaev
• Grantee: Makar Plakhotnyk
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 15/09162-9 - Non commutative algebra and applications, AP.TEM

Abstract

The project will be dedicated to the study of exponent matrixes of tiled orders and some aspects of the theory of partial actions. More precisely, we will consider the problem of the classification of exponent matrixes, mainly via study of minimal non-negative exponent matrixes, with special attention payed to (0,1)-matrixes. We wil also investigate the exponent matrixes of tiled orders which satisfy such homological properties as to be a hereditary order or a Gorenstein order. With respect to the theory of partial actions the candidate will participate the working group in cohomological theory based on partial actions, studying questions on projective and injective objects, as well as problems related to the homological dimension in partial setting. Moreover, the cohomology groups with values in specific partial G-modules will be computed for some concrete groups G, producing testing material for conjectures and ideas.

Scientific publications

(4)

(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)

PLAKHOTNYK, MAKAR. The Derivative of the Conjugacy Between Skew Tent Maps. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 28, n. 9, AUG 2018. (13/11350-2)

DUDCHENKO, IRYNA; PLAKHOTNYK, MAKAR. On indices and eigenvectors of quivers. ALGEBRA & DISCRETE MATHEMATICS, v. 27, n. 1, SI, p. 12-19, 2019. (13/11350-2)

DOKUCHAEV, MIKHAILO; KIRICHENKO, VLADIMIR; KUDRYAVTSEVA, GANNA; PLAKHOTNYK, MAKAR. The max-plus algebra of exponent matrices of tiled orders. Journal of Algebra, v. 490, p. 1-20, NOV 15 2017. (15/09162-9, 13/11350-2, 15/16726-6, 14/23853-1)

DUDCHENKO, IRYNA; PLAKHOTNYK, MAKAR. On indices and eigenvectors of quivers. ALGEBRA & DISCRETE MATHEMATICS, v. 27, n. 1, p. 8-pg., 2019-01-01. (13/11350-2)