General Poisson algebras and generalized derivarions

• Grant number: 11/51132-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2011
• End date: August 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Chestakov
• Grantee: Ivan Kaygorodov
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The research project is for the post-doc program in algebra. Derivations, automorphisms, an analog of the Bergman Centralized Theorem and analogs of Makar-Limanov's results for free Poisson algebras will be considered for free general (non-Lie-admissible) Poisson algebra. Also, the algebras of delta-derivations of some simple finite-dimensional Filippov algebras and ternary Malcev algebra M_8 will be investigated. The results of the project can be used in studies of general Poisson algebras, nonassociative n-ary algebras, Nambu mechanics and other applications. (AU)

Scientific publications

(7)

(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)

KAYGORODOV, IVAN; OKHAPKINA, ELIZAVETA. delta-DERIVATIONS OF SEMISIMPLE FINITE-DIMENSIONAL STRUCTURABLE ALGEBRAS. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 13, n. 4, JUN 2014. (11/51132-9)

KAYGORODOV, I. B.. On delta-derivations of n-ary algebras. IZVESTIYA MATHEMATICS, v. 76, n. 6, p. 1150-1162, 2012. (11/51132-9)

KAYGORODOV, I. B.; POPOV, YU. S.. Alternative algebras admitting derivations with invertible values and invertible derivations. IZVESTIYA MATHEMATICS, v. 78, n. 5, p. 922-936, 2014. (11/51132-9)

KAIGORODOV, I. B.. ON (n+1)-ARY DERIVATIONS OF SIMPLE n-ARY MAL'TSEV ALGEBRAS. ST PETERSBURG MATHEMATICAL JOURNAL, v. 25, n. 4, p. 575-585, AUG 2014. (11/51132-9)

KAYGORODOV, IVAN; LOPATIN, ARTEM; POPOV, YURY. Conservative algebras of 2-dimensional algebras. Linear Algebra and its Applications, v. 486, p. 255-274, DEC 1 2015. (11/51132-9)

KAYGORODOV, I. B.. (n+1)-ary derivations of semisimple Filippov algebras. MATHEMATICAL NOTES, v. 96, n. 1-2, p. 208-216, JUL 2014. (11/51132-9)

KAYGORODOV, I. B.. delta-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras. MATHEMATICAL NOTES, v. 91, n. 1-2, p. 187-197, FEB 2012. (11/51132-9)