bachelor's at Mathematics from Sofia University "St. Kliment Okhridski" (1981), master's at algebra from Sofia University "St. Kliment Okhridski" (1983) and doctorate at algebra from Sofia University "St. Kliment Okhridski" (1987). Has experience in Mathematics, acting on the following subjects: graded identities, t-ideal, identidades polinomiais, propriedade de specht and bases of identities. (Source: Lattes Curriculum)
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Most of the project will be dedicated to Lie and Jordan algebras and superalgebras and their representations. In addition, Malcev and alternative algebras and superalgebras will be considered, Moufang loops and various generalizations and applications of above. Algebraic systems related to integrable systems of differential equations will be considered. Homological methods will be applied…
(Only some records are available in English at this moment)
In this project for PhD research we shall study topics in the theory of algebras with polynomial identities. The notion of a regular algebra was introduced by Regev and Seeman, and afterwards was studied by Bahturin and Regev, and various other researchers. The decomposition of a regular algebra into a (finite) direct sum of vector subspaces satisfying certain properties (see below) can o…
In this research project towards MSc degree in Mathematics we study certain classical topics of the theory of algebras with polynomial identities. We shall start with a brief overview of polynomial identities, PI algebras, varieties of algebras, T-ideals, linearization, homogeneous and multilinear structure of relatively free algebras, representation theory of the symmetric and of the gen…
We shall study the fundaments of the theory of noncommutative rings. We shall cover division rings and the Frobenius theorem about the quaternion algebra. The Wedderburn theorem concerning the commutativity of finite division rings will be covered as well. We shall see also the notion of a central simple algebra. The Skolem-Noether theorem about the automorphisms will be a central piece i…
(Only some records are available in English at this moment)
We will study some topics in the Theory of algebras satisfying polynomial identities in this proposal for a Master Degree. We will approach the basics of the theory, namely polynomial identities, PI algebras, varieties of algebras, T-ideals, the linearization process, the homogeneous and the multilinear structures of relatively free algebras. To this end we shall need some facts from Ring…
In tis project we shall study some topics of significant relevance for Contemporary Algebra. First we shall study some basic notions of Group Theory, mainly finite groups. Afterwards we approach elements of Field Theory and extensions, using the language of polynomials and roots. We shall cover finite, algebraic, f.g. extensions. Then we pass to symmetric polynomials and roots, and their …
In this research project, we aim at studying some of the basic notions of Contemporary Algebra. We are commencing with a brief revision of Group Theory (the student has already studied the basics of the area, and he did a formal study as a Introduction to Science, and moreover, now he is studying topics of Group Theory). Afterwards we will continue with the Representation Theory of finite…
(Only some records are available in English at this moment)
The Lvov-Kaplansky conjecture states that the image of a multilinear polynomial on the full matrix algebra is a vector subspace. The purpose of this research project is to study a variation of the aforementioned conjecture in the context of multilinear polynomials on the involution algebras UT_2 and UT_3. (AU)
We shall study the graded identities for an elementary grading on the Lie algebra of upper triangular matrices. To this end we shall study the combinatorial properties of certain subset of the permutation group of m elements. Moreover we are planning to approach the following problem. Given two finite dimensional graded simple Lie algebras over an algebraically closed field, satisfying th…
| 1 / 1 | Ongoing research grants |
| 18 / 11 | Completed research grants |
| 6 / 6 | Ongoing scholarships in Brazil |
| 11 / 7 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 1 / 1 | Completed scholarships abroad |
| 38 / 27 | All research grants and scholarships |
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CV Lattes
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