IK has bachelor degree in mathematics from Kiev University (1997), master degree in mathematics from University of Kaiserslautern (2000) and doctorate in mathematics from Universidade de São Paulo (2004). Has experience in mathematics, acting on the following subjects: representations of Lie and Jordan algebras and superalgebras, free Jordan algebras, affine Lie algebras, toroidal Lie algebras. (Source: Lattes Curriculum)
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This is a research project in the area of Algebra. The project is divided into three parts. The first part is dedicated to the study of representations of Jordan algebras and superalgebras.The second part of the project concerns the investigation of the free Jordan algebra J(n) with n generators, more exactly the structure of the homogeneous component J(n)d of degree d as GL(d)-module. In…
The goal of this project is to explore the category of finite-dimensional representations of the periplectic Lie superalgebra $\hat{\mathfrak{p}}(3)$ with non-trivial central charge. (AU)
This project in area of Algebra and consists of the following parts. In first one, the main goal is to study the categories of indecomposable representations of finite dimension over Lie and Jordan(super)algebras.In the next part, we want to understand the algebras of Moufang-Hopf, a generalization of the universal enveloping algebras of Lie algebras. The final part deals with the Lie alg…
The main goal of this project is the study of combinatorial aspects of the representation theory of Lie Algebras, in particular their cuspidal representations. In a remarkable paper, O. Mathieu classified the irreducible weight modules by classifying cuspidal representations via coherents families. In his work, the author obtained combinatorial properties such as a formula for the degree …
The main objective of this postdoctoral project is to study the representations of symmetrizable twisted affine Lie Superalgebras and, in particular, to develop the theory of Verma modules and generalized Verma modules for these algebras. In addition, we intend to extend the results to the quantum case and study the representations of the finite W-Superalgebras obtained through the Hamilt…
This project is for Master program in the area of algebra. The goal of this project is to study the structure and representation theory of affine wreath product algebras. These algebras appear naturally in Heisenberg categorification and generalize many important algebras (degenerate Hecke algebras, affine Sergeev algebras and wreath Hecke algebras). The whole class was introduced by D. R…
It is a research project for the Cientific Iniciation program in Algebra. The project is aimed for the student of Bachelor of Mathematics aims as main topic introduction of concepts and elementary principles of Algebraic Geometry, extending the knowledge already obtained in Abstract and Linear Algebra courses, passing through vector spaces, matrix rings and polynomials to modules over com…
The goal of this project is to study combinatoric aspects of irreducible cuspidal representations of a simple lie algebra g and their relation with g-modules that are finitely generated by the universal envelop algebra of h, a fixed Cartan sub algebra of g. Cuspidal representation was classified by Olivier Mathieu, that also gave a formula for their weight spaces dimensions. We intend to …
The goal of this project is to study the representation theory of affine wreath product algebras. These algebras appear naturally in Heisenberg categorification and generalize many important algebras (degenerate affine Hecke algebras, affine Sergeev algebras and wreath Hecke algebras). The whole class was introduced by D. Rosso and A. Savage. The second author studied both structure and r…
The goal of this project is to explore relationship between representations of a Jordan (super)algebra J and a graded Lie (super)algebra g obtained from J by the Tits-Kantor-Koecher construction. The representation theory of Jordan and especially Lie superalgebras was used in theoretical physics to describe the mathematics of supersymmetry and since the became a prominent field with the n…
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing research grants |
| 2 / 2 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 5 / 3 | Completed scholarships in Brazil |
| 4 / 4 | Completed scholarships abroad |
| 13 / 11 | All research grants and scholarships |
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