Thesis supervisor: Péter Tibor Nagy
Location of studies (in Hungarian): Óbuda University Abbreviation of location of studies: ÓE
Description of the research topic:
Groups with operations defined by differentiable mappings are called Lie groups. In the classical theory, it is proved that the real-analytic property of these group operations follows from the associativity. Therefore, in a suitable coordinate system around the identity element, the multiplication map can be expanded into a convergent power series, which is called the Campbell-Hausdorff series. The coefficients of this series are determined by the coefficients of the terms of second order, these terms define an anticommutative algebra on the tangent space, called the Lie algebra. In recent decades, a large number of studies have been devoted to various non-associative generalizations of such groups, which are called loops. The theory of Lie loops is richer than the theory of groups, since in their case analyticity does not follow from the differentiability of operations. A tangent algebra, called Akivis algebra, can also be introduced on the tangent space of loops. As part of the research task, Taylor polynomials of the multiplication operation and the corresponding Akivis algebras for specific classes of loops will be investigated, and vice versa, to what extent do the Akivis algebras determine the multiplication operation. The planned research requires the basic methods of differential geometry, algebra and function theory.
Required language skills: English Number of students who can be accepted: 1
Deadline for application: 2023-05-01
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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