Lie Algebras over a field of positiv characteristic and their deformations
Mikhail Vladimirovich Zaicev | Moscow State University - Rússia
On maps preserving some identities on nonassociative algebraic structures
| Grant number: | 18/00726-5 |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| Start date: | July 15, 2018 |
| End date: | 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)
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