Classi cation of 5−dimensional complex nilpotent Leibniz algebras
Başlık çevirisi mevcut değil.
- Tez No: 403082
- Danışmanlar: DR. KAILASH MISRA, DR. ERNEST STITZINGER
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2016
- Dil: İngilizce
- Üniversite: North Carolina State University
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 145
Özet
Özet yok.
Özet (Çeviri)
Leibniz algebras are certain generalization of Lie algebras. They were introduced by Bloh (1965) who called them D-algebras. Then it was popularized by Loday (1993) and the subject has been studied since then. Lie algebras are known to have many applications in mathematical areas including algebraic geometry, di erential geometry, di erential equations, number theory and also in physical areas such as general relativity, quantum mechanics, quantum eld theory, string theory, particle physics and nuclear physics. The classi cation problem is one of the fundamental and important problems in Lie algebras. The famous Levi-Malcev (1905, 1950) theorem reduce the problem of classifying Lie algebras to classifying semisimple and solvable Lie algebras over a eld of characteristic 0. The semisimple Lie algebras was classi ed by Cartan (1894) and later re ned by Dynkin (1947). Malcev (1950) showed that the problem of classifying solvable Lie algebras can be reduced to classifying nilpotent Lie algebras. So far the complete classi cation of complex nilpotent Lie algebras of dimension n B 7 is known and the classi cation problem of complex nilpotent Lie algebras is wild in higher dimensions. The lack of antisymmetry property in Leibniz algebras makes the classi cation problem more dicult for Leibniz algebras. In this work, we give the classi cation of complex nilpotent non-split non-Lie Leibniz algebras of dimension n B 5. A Leibniz algebras is called non-split if it doesn't have nontrivial ideals as a summand. We introduce the technique involving bilinear forms to obtain the classi cation of complex nilpotent non-split non-Lie Leibniz algebras with one dimensional derived algebra. The remaining cases are done by using some algebraic invariants.
Benzer Tezler
- Biyomedikal görüntülerin sınıflandırılması için yeni bir evrişimli sinir ağı mimarisi
A novel convolutional neural network architecture for classification of biomedical images
ÖZNUR ÖZALTIN
Doktora
Türkçe
2023
İstatistikHacettepe Üniversitesiİstatistik Ana Bilim Dalı
PROF. DR. MURTAZA ÖZGÜR YENİAY
DR. ORHAN ÇOŞKUN
- Multispektral İHA verilerinin obje tabanlı sınıflandırılmasında ndym tabanlı performans artırım yaklaşımları
Ndsm-based potential enhancement approaches in object-based classification of multispectral uav data
İLYAS AYDIN
Yüksek Lisans
Türkçe
2024
Jeodezi ve FotogrametriGebze Teknik ÜniversitesiHarita Mühendisliği Ana Bilim Dalı
PROF. DR. UMUT GÜNEŞ SEFERCİK
- İstanbul'daki Sinan camilerinde mekan ile serbest düşey taşıyıcılar arasındaki boyut ilişkisi
The Relationship between space and independent vertical load-bearers at Sinan's mosques in İstanbul
ŞÜKRÜ SÖNMEZER
- Gemilerin ısar ile görüntülenmesinde radar saçılma yüzeylerinin fizik optik yardımıyla modellenmesi
Başlık çevirisi yok
E.ELİF TEPELİ
Yüksek Lisans
Türkçe
1995
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiPROF.DR. ERCAN TOPUZ