The classification of three-dimensional homogeneous complex manifolds X=G/H where G is a complex lie group

1995 ◽  
pp. 20-84
Author(s):  
Jörg Winkelmann
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Complex Manifolds ◽  
Homogeneous Complex

scholarly journals On closed radical orbits in homogeneous complex manifolds

1996 ◽  
Vol 54 (3) ◽  
pp. 363-368 ◽  
Author(s):  
Bruce Gilligan
Keyword(s):  
Finite Number ◽  
Lie Group ◽  
Discrete Subgroup ◽  
Connected Components ◽  
Complex Manifolds ◽  
Algebraic Subgroup ◽  
Homogeneous Complex ◽  
Semisimple Complex ◽  
Klein Form

Suppose G is a complex Lie group having a finite number of connected components and H is a closed complex subgroup of G with H° solvable. Let RG denote the radical of G. We show the existence of closed complex subgroups I and J of G containing H such that I/H is a connected solvmanifold with I° ⊃ RG, the space G/J has a Klein form SG/A, where A is an algebraic subgroup of the semisimple complex Lie group SG: = G/RG, and, unless I = J, the space J/I has Klein form , where is a Zariski dense discrete subgroup of some connected positive dimensional semisimple complex Lie group Ŝ.

Homogeneous Complex Manifolds with more than One End

1989 ◽  
Vol 41 (1) ◽  
pp. 163-177 ◽  
Author(s):  
B. Gilligan ◽  
K. Oeljeklaus ◽  
W. Richthofer
Keyword(s):  
Lie Group ◽  
Homogeneous Spaces ◽  
Maximal Compact Subgroup ◽  
Compact Subgroup ◽  
Complex Manifolds ◽  
Connected Subgroup ◽  
Homogeneous Complex ◽  
Homogeneous Complex Manifold ◽  
Homogeneous Cone ◽  
Closed Connected Subgroup

For homogeneous spaces of a (real) Lie group one of the fundamental results concerning ends (in the sense of Freudenthal [8] ) is due to A. Borel [6]. He showed that if X = G/H is the homogeneous space of a connected Lie group G by a closed connected subgroup H, then X has at most two ends. And if X does have two ends, then it is diffeomorphic to the product of R with the orbit of a maximal compact subgroup of G.In the setting of homogeneous complex manifolds the basic idea should be to find conditions which imply that the space has at most two ends and then, when the space has exactly two ends, to display the ends via bundles involving C* and compact homogeneous complex manifolds. An analytic condition which ensures that a homogeneous complex manifold X has at most two ends is that X have non-constant holomorphic functions and the structure of such a space with exactly two ends is determined, namely, it fibers over an affine homogeneous cone with its vertex removed with the fiber being compact [9], [13].

scholarly journals Three-dimensional connected groups of automorphisms of toroidal circle planes

2020 ◽  
Vol 20 (4) ◽  
pp. 585-594
Author(s):  
Brendan Creutz ◽  
Duy Ho ◽  
Günter F. Steinke
Keyword(s):  
Lie Group ◽  
Three Dimensional ◽  
Minkowski Planes ◽  
Point Set ◽  
Groups Of Automorphisms ◽  
Full Classification

AbstractWe contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to PSL(2, ℝ). Using this result, we describe a framework for the full classification based on the action of the group on the point set.

scholarly journals Topological Loops with Decomposable Solvable Multiplication Groups

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Ameer Al-Abayechi ◽  
Ágota Figula
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Three Dimensional ◽  
Solvable Lie Groups ◽  
3 Dimensional ◽  
Multiplication Group ◽  
Simply Connected ◽  
Solvable Lie Group

AbstractIn this paper we deal with the class $$\mathcal {C}$$ C of decomposable solvable Lie groups having dimension six. We determine those Lie groups in $$\mathcal {C}$$ C and their subgroups which are the multiplication groups Mult(L) and the inner mapping groups Inn(L) for three-dimensional connected simply connected topological loops L. This result completes the classification of the at most 6-dimensional solvable multiplication Lie groups of the loops L. Moreover, we obtain that every at most 3-dimensional connected topological proper loop having a solvable Lie group of dimension at most six as its multiplication group is centrally nilpotent of class two.

Phonetic iconicity in the evaluative morphology of a sample of Indo-European, Niger-Congo and Austronesian languages

2010 ◽  
Vol 3 (2) ◽  
pp. 156-180 ◽  
Author(s):  
Renáta Gregová ◽  
Lívia Körtvélyessy ◽  
Július Zimmermann
Keyword(s):  
Three Dimensional ◽  
Sound Symbolism ◽  
Three Dimensional Model ◽  
Austronesian Languages ◽  
Place Of Articulation ◽  
European Languages ◽  
Phonetic Symbolism ◽  
The Individual ◽  
Core Vocabulary

Universals Archive (Universal #1926) indicates a universal tendency for sound symbolism in reference to the expression of diminutives and augmentatives. The research ( Štekauer et al. 2009 ) carried out on European languages has not proved the tendency at all. Therefore, our research was extended to cover three language families – Indo-European, Niger-Congo and Austronesian. A three-step analysis examining different aspects of phonetic symbolism was carried out on a core vocabulary of 35 lexical items. A research sample was selected out of 60 languages. The evaluative markers were analyzed according to both phonetic classification of vowels and consonants and Ultan's and Niewenhuis' conclusions on the dominance of palatal and post-alveolar consonants in diminutive markers. Finally, the data obtained in our sample languages was evaluated by means of a three-dimensional model illustrating the place of articulation of the individual segments.

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