Deformations of nonassociative algebras

• Grant number: 18/00726-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Duration: July 15, 2018 - August 29, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ivan Kaygorodov
• Grantee: Ivan Kaygorodov
• Visiting researcher: Pasha Zusmanovich
• Visiting researcher institution: University of Ostrava, Czech Republic
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

The project is about non-associative algebras. During the realization of the project we are planning. (1) Describe deformations of the current Lie algebras of the form Ln A in terms of deformations and other invariants of the algebra A. (2) To investigate properties of binary quadratic operads for which the dual operad coincides with the "opposite" operad, and investigate properties of algebras over those operads. (3) To investigate deformations and cohomology of affinizations of Novikov algebras, and, more generally, of Lie algebras formed as the direct product of a left Novikov and a right Novikov algebra. (4) To find which "interesting", from the viewpoint of structure theory, and of applications in physics, Lie algebras admit a representation as the tensor product of a mock Lie algebra and an anticommutative antiassociative algebra, and compute deformations and cohomology of such algebras. (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)

KAYGORODOV, IVAN; KHRYPCHENKO, MYKOLA. The algebraic classification of nilpotent CD-algebras. LINEAR & MULTILINEAR ALGEBRA, DEC 2020. (18/15712-0, 18/00726-5)

KAYGORODOV, IVAN; KHRYPCHENKO, MYKOLA. The geometric classification of nilpotent CD-algebras. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 20, n. 11, NOV 2021. (18/15712-0, 18/00726-5)

KAYGORODOV, IVAN; KHRYPCHENKO, MYKOLA. The algebraic classification of nilpotent CD-algebras. LINEAR & MULTILINEAR ALGEBRA, v. 70, n. 19, p. 47-pg., 2020-12-05. (18/00726-5, 18/15712-0)