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Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Alexandre Grichkov in research grants and scholarships supported by FAPESP.
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The main part of the project will be devoted to associative, Lie and Jordan algebras and superalgebras and their representations. In addition, alternative and Malcev algebras and superalgebras, Moufang loops and several generalizations will be considered. The main topics are: 1) Representations of Kac-Moody algebras; 2) Homological and homotopic properties and discrete group theory, pro-p…
A geometric description of a class of integrable evolution PDE systems involves anane connection and a covariantly constant tensor of rank (1; 3). Integrability imposes strongconditions on both the ane connection and on the tensor. In particular, the tensor turns outto be a deformation of a triple Jordan system. The goal of the project is an investigation of theabove geometrical structure…
Let A = FG be the group algebra of a finite group G over a field F. Our aim is investigate the properties of Rota-type operators on the modular group algebra FG, i.e. algebras in which the characteristic of the ground field F divides the order of the group G. Of particular interest is the case when the characteristic of F is two. (AU)
Task 1: Symmetry analysis of the governing equation for the $n$-point PDF $f_n$ for passive scalar fields based on the direct method. Task 2: Conformal invariance of the probability measure. Task 3: The derivation of a Lie group of the symmetry transformations calculated. Task 4: The fine structure of a Lie algebra to classify the zero-isolines by the central charge. Then the effects …
(Only some records are available in English at this moment)
Automorphic loops. Let L be a loop and G the multiplication group of loop L, generated by left and right multiplication operators. We denote H(L) = StabG(L)(e), where ex = xe = x. The loop L is called automorph if H(L) is in Aut(L). There are few explicit constructions of automorph loops. The problem of calculating H(L) groupsand Aut(L) are still open.We emphasize that this problem is rel…
The main goal of the project is a study of the Representation Theory of W-algebras. We are planning to obtain new classes of representations of W-algebras from known representations of Kac-Moody algebras, to develop the Gelfand-Tsetlin theory for W-algebras and Affine Kac-Moody algebras and apply the theory of Galois algebras para study of representations of both finite and affine W-algeb…
The main object of the Project is to recieve significant results about finite geometries with three points on any line. In particulary:1) we want to study finite geometries and corresponding free loops and thier automorphisms,2) describe the arbitrary (and central)extentions of those loops,3) describe the Steiner loops, corresponding to geometries with three points on the line, with mini…
(Only some records are available in English at this moment)
During this period we intend to work on the following topics: 1. Simple Lie algebras over a field of characteristic 2. 2. Commutative Moufang Loops. 3. Code loops. 4. Steiner loops and finite geometries. 5. The finite exponent loop growth problem. 6. Malcev algebras and Moufang loopsanalytics. 7. Quasivariety of loops. As a main result of the visit, we hope to submit at least 3 articles, …
We expect to obtaint significant results in the following directions: 1. Lie algebras:a) to classify simple Lie algebras of dimension < 8 and 2-algebras of di-mension < 16:b) classify simple finite dimensional Lie algebras of toral rank two in char-acteristic 2.c) construct new simple finite dimensional Lie algebras and 2-algebras,d) describe the simple Lie algebras in characteristic 2 wi…
| 1 / 1 | Ongoing grants |
| 43 / 30 | Completed research grants |
| 7 / 6 | Completed scholarships in Brazil |
| 4 / 2 | Completed scholarships abroad |
| 55 / 39 | All research grants and scholarships |
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