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Analysis on the Heisenberg group

Małgorzata Łazęcka

Abstract

This survey is devoted to the Heisenberg group. We show that the Lebesgue measure is left invariant with respect to the group law on the Heisenberg group. We calculate the Lie algebra of the Heisenberg group by finding left invariant vector fields. Two metrics on the Heisenberg group are introduced (Carnot-Caratheodory metric and Koranyi metric) and we show their equivalence. We find Hausdorff dimension of the Heisenberg group.
Diploma type
Engineer's / Bachelor of Science
Diploma type
Bachelor thesis
Author
Małgorzata Łazęcka (FMIS) Małgorzata Łazęcka,, Faculty of Mathematics and Information Science (FMIS)
Title in Polish
Analiza na grupie Heisenberga
Supervisor
Przemysław Górka (FMIS/DPDE) Przemysław Górka,, Department of Partial Differential Equations (FMIS/DPDE)Faculty of Mathematics and Information Science (FMIS)
Certifying unit
Faculty of Mathematics and Information Science (FMIS)
Affiliation unit
Department of Partial Differential Equations (FMIS/DPDE)
Study subject / specialization
, Matematyka
Language
(pl) Polish
Status
Finished
Defense Date
21-09-2016
Issue date (year)
2016
Reviewers
Przemysław Górka (FMIS/DPDE) Przemysław Górka,, Department of Partial Differential Equations (FMIS/DPDE)Faculty of Mathematics and Information Science (FMIS) Bogusława Karpińska (FMIS/DODE) Bogusława Karpińska,, Department of Ordinary Differential Equations (FMIS/DODE)Faculty of Mathematics and Information Science (FMIS)
Keywords in Polish
grupa Heisenberga, grupa Liego, algebra Liego, metryka Carnot-Caratheodory'ego, metryka Koranyi, twierdzenie Chow-Rashevsky'ego, wymiar Hausdorffa
Keywords in English
Heisenberg group, Lie group, Lie algebra, Carnot-Caratheodory metric, Koranyi metric, Chow-Rashevsky's theorem, Hausdorff dimension
Abstract in Polish
Praca poświęcona jest grupie Heisenberga. Wykazano, że miara Lebesgue'a jest miarą niezmienniczą na przesunięcia na grupie Heisenberga. Policzono algebrę Liego grupy Heisenberga, tzn. znaleziono pola lewoniezmiennicze. Wprowadzono dwie metryki na grupie Heisenberga (metrykę Carnot-Caratheodory'ego i Koranyi) i pokazano ich równoważność. Znaleziono wymiar Hausdorffa grupy Heisenberga.
File
  • File: 1
    Analiza na grupie Heisenberga.pdf
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Local fields
Identyfikator pracy APD: 9170

Uniform Resource Identifier
https://repo.pw.edu.pl/info/bachelor/WUT84eafa17535a4e0bb8e3e8ef4a5c4c94/
URN
urn:pw-repo:WUT84eafa17535a4e0bb8e3e8ef4a5c4c94

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