scholarly journals On completeness of holomorphic principal bundles

1975 ◽  
Vol 56 ◽  
pp. 121-138 ◽  
Author(s):  
Shigeru Takeuchi
Keyword(s):  
Algebraic Group ◽  
Lie Groups ◽  
Abelian Variety ◽  
Lie Group ◽  
Basic Structure ◽  
Factor Group ◽  
The Other ◽  
Algebraic Subgroup ◽  
Points Of View ◽  
Lie Subgroup

In this paper we shall investigate the structure of complex Lie groups from function theoretical points of view. A. Morimoto proved in [10] that every connected complex Lie group G has the smallest closed normal connected complex Lie subgroup Ge, such that the factor group G/Ge is Stein. On the other hand there hold the following two basic structure theorems (A1) and (A2) for a connected algebraic group G (cf. [12]). (A1): G has the smallest normal algebraic subgroup N such that the factor group G/N is an affine algebraic group. Moreover N is a connected central subgroup. (A2): G has the unique maximal connected affine algebraic subgroup L, where L is normal and the factor group G/L is an abelian variety.

scholarly journals Fixed points of Lie group actions on surfaces

1986 ◽  
Vol 6 (1) ◽  
pp. 149-161 ◽  
Author(s):  
J. F. Plante
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Lie Groups ◽  
Euler Characteristic ◽  
Lie Group ◽  
Stationary Point ◽  
Compact Surface ◽  
The Other ◽  
Continuous Action ◽  
Finite Dimensional

AbstractLetGbe a connected finite-dimensional Lie group andMa compact surface. We investigate whether, for a givenGandM, every continuous action ofGonMmust have a fixed (stationary) point. It is shown that whenGis nilpotent andMhas non-zero Euler characteristic that every action ofGonMmust have a fixed point. On the other hand, it is shown that the non-abelian 2-dimensional Lie group (affine group of the line) acts without fixed points on every compact surface. These results make it possible to complete this investigation for Lie groups of dimension at most 3.

scholarly journals Some remarks on complex Lie groups

2000 ◽  
Vol 157 ◽  
pp. 47-57
Author(s):  
H. Kazama ◽  
D. K. Kim ◽  
C. Y. Oh
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Group ◽  
Exhaustion Function ◽  
The Real ◽  
Lie Subgroup

First we show that any complex Lie group is complete Kähler. Moreover we obtain a plurisubharmonic exhaustion function on a complex Lie group as follows. Let the real Lie algebra of a maximal compact real Lie subgroup K of a complex Lie group G. Put q := dimC Then we obtain that there exists a plurisubharmonic, strongly (q + 1)-pseudoconvex in the sense of Andreotti-Grauert and K-invariant exhaustion function on G.

scholarly journals On orbits of algebraic groups and Lie groups

1982 ◽  
Vol 25 (1) ◽  
pp. 1-28 ◽  
Author(s):  
R.W. Richardson
Keyword(s):  
Fixed Points ◽  
Homogeneous Space ◽  
Algebraic Group ◽  
Lie Groups ◽  
Lie Group ◽  
Closed Subgroup ◽  
Algebraic Groups ◽  
General Situation ◽  
Coset Space ◽  
Identity Component

In this paper we will be concerned with orbits of a closed subgroup Z of an algebraic group (respectively Lie group) G on a homogeneous space X for G. More precisely, let D be a closed subgroup of G and let X denote the coset space G/D. Let S be a subgroup of G and let Z denote (GS)0 the identity component of GS, the centralizer of S in G. We consider the orbits of Z on XS, the set of fixed points of S on X. We also treat the more general situation in which S is an algebraic group (respectively Lie group) which acts on G by automorphisms and acts on X compatibly with the action of G; again we consider the orbits of (GS)0 on XS.

Sin is Dead, Long Live Sin!

2017 ◽  
Author(s):  
Kate Kirkpatrick
Keyword(s):  
Religious Commitment ◽  
The Other ◽  
Realist Approach ◽  
Points Of View ◽  
Cultural Amnesia

Chapter 9 offers two concluding ‘provocations’: one on wretchedness without God, the other on wretchedness with God. The first brings Sartre into dialogue with Marilyn McCord Adams’s work ‘God because of Evil’, arguing that Sartre’s account lends credence to her view that optimism is not warranted if one takes a robust realist approach to evil. Read as a phenomenologist of fallenness, Sartre may serve the apologetic purpose of making options ‘live’, in William James’s language; or, to use the phrase of Stephen Mulhall, to ‘hold open the possibility of taking religious points of view seriously’. The second provocation—on the question of wretchedness with God—suggests that Sartre can be read ‘for edification’ to help us see our failures in love. The book concludes that reading Sartre in this light can help redress ‘damaging cultural amnesia’ about religious commitment, offering an account of sin that cultivates humility, love, and mercy.

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

scholarly journals The Higher Order Riesz Transform andBMOType Space Associated with Schrödinger Operators on Stratified Lie Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yu Liu ◽  
Jianfeng Dong
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Riesz Transform ◽  
Integral Operators ◽  
Higher Order ◽  
Reverse Hölder Class ◽  
Stratified Lie Group ◽  
Homogeneous Dimension ◽  
Stratified Lie Groups ◽  
Reverse Hölder

Assume thatGis a stratified Lie group andQis the homogeneous dimension ofG. Let-Δbe the sub-Laplacian onGandW≢0a nonnegative potential belonging to certain reverse Hölder classBsfors≥Q/2. LetL=-Δ+Wbe a Schrödinger operator on the stratified Lie groupG. In this paper, we prove the boundedness of some integral operators related toL, such asL-1∇2,L-1W, andL-1(-Δ) on the spaceBMOL(G).

ON THE MODEL THEORY OF THE LOGARITHMIC FUNCTION IN COMPACT LIE GROUPS

2013 ◽  
Vol 12 (08) ◽  
pp. 1350055
Author(s):  
SONIA L'INNOCENTE ◽  
FRANÇOISE POINT ◽  
CARLO TOFFALORI
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Model Theory ◽  
Effective Model ◽  
Logarithmic Function ◽  
Compact Lie Groups ◽  
Model Completeness ◽  
Schanuel's Conjecture ◽  
Logarithm Function ◽  
Natural Expansion

Given a compact linear Lie group G, we form a natural expansion of the theory of the reals where G and the graph of a logarithm function on G live. We prove its effective model-completeness and decidability modulo a suitable variant of Schanuel's Conjecture.

Combinatorial principles weaker than Ramsey's Theorem for pairs

2007 ◽  
Vol 72 (1) ◽  
pp. 171-206 ◽  
Author(s):  
Denis R. Hirschfeldt ◽  
Richard A. Shore
Keyword(s):  
Reverse Mathematics ◽  
The Other ◽  
Base System ◽  
Ramsey's Theorem ◽  
Open Questions ◽  
Ramsey’S Theorem ◽  
Combinatorial Principles ◽  
Points Of View ◽  
The One ◽  
Infinite Linear

AbstractWe investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is wellknown that Ramsey's Theorem for pairs () splits into a stable version () and a cohesive principle (COH). We show that the same is true of ADS and CAC, and that in their cases the stable versions are strictly weaker than the full ones (which is not known to be the case for and ). We also analyze the relationships between these principles and other systems and principles previously studied by reverse mathematics, such as WKL0, DNR, and BΣ2. We show, for instance, that WKL0 is incomparable with all of the systems we study. We also prove computability-theoretic and conservation results for them. Among these results are a strengthening of the fact, proved by Cholak, Jockusch, and Slaman, that COH is -conservative over the base system RCA0. We also prove that CAC does not imply DNR which, combined with a recent result of Hirschfeldt, Jockusch. Kjos-Hanssen, Lempp, and Slaman, shows that CAC does not imply (and so does not imply ). This answers a question of Cholak, Jockusch, and Slaman.Our proofs suggest that the essential distinction between ADS and CAC on the one hand and on the other is that the colorings needed for our analysis are in some way transitive. We formalize this intuition as the notions of transitive and semitransitive colorings and show that the existence of homogeneous sets for such colorings is equivalent to ADS and CAC, respectively. We finish with several open questions.

THE FERMI–WALKER DERIVATIVE IN LIE GROUPS

2013 ◽  
Vol 10 (07) ◽  
pp. 1320011 ◽  
Author(s):  
FATMA KARAKUŞ ◽  
YUSUF YAYLI
Keyword(s):  
Vector Field ◽  
Lie Groups ◽  
Lie Group ◽  
Necessary Conditions ◽  
Rotating Frame ◽  
Darboux Vector

In this study, Fermi–Walker derivative, Fermi–Walker parallelism, non-rotating frame, Fermi–Walker termed Darboux vector concepts are given for Lie groups in E4. First, we get any Frénet curve and any vector field along the Frénet curve in a Lie group. Then, the Fermi–Walker derivative is defined for the Lie group. Fermi–Walker derivative and Fermi–Walker parallelism are analyzed in Lie groups. Finally, the necessary conditions for Fermi–Walker parallelism are explained.

scholarly journals To Publish, Make Known and Sell or Promoting Printed Books in the Incunabula Period

2021 ◽  
Vol 15 (3) ◽  
pp. 331-356
Author(s):  
Lucia Lichnerová
Keyword(s):  
Geographical Area ◽  
The Other ◽  
Book Production ◽  
Book Market ◽  
Design Elements ◽  
15Th Century ◽  
Other Hand ◽  
Printed Books ◽  
Points Of View ◽  
The One

The study To Publish, Make Known and Sell is based on verified existence of competition tensions between the 15th century typographers/publishers, related to the absence of functional regulatory tools of book production of the incunabula period. The increase in the number of book-printers within the relatively narrow geographical area, disregard of publishers’ privileges, the emergence of pirated reprints, as well as insufficient self-promotion on the book market through introducing novelties had concentrated typographers’ attention on devising new tools of securing their triumph in publisher’s competition – the so called book advertisements. The author has analysed 44 promotional posters of the incunabula period from several points of view and attempted to identify their design elements, which on the one hand showed signs of certain standardization, while on the other hand they were subject to personal creativity of their creator. She gives detailed overview of the circumstances of the origin, typographic design and contents of book advertisements of several kinds within the context of promoting either the existing or planned editions, of one edition or a group of books; specifically focusing on the unique types of advertising. In conclusion, the author cites the circumstances of the extinction of book advertisements related to the rise of the new promotional tool – booksellers’ catalogue and submits a bibliography of the book advertisements dating from the 15th century.

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