Left Invariant Einstein–Randers Metrics on Compact Lie Groups

2012 ◽  
Vol 55 (4) ◽  
pp. 870-881 ◽  
Author(s):  
Hui Wang ◽  
Shaoqiang Deng
Keyword(s):  
Lie Groups ◽  
Complete Classification ◽  
Simple Groups ◽  
Compact Lie Group ◽  
Compact Lie Groups ◽  
Navigation Data ◽  
Group Of Isometries ◽  
Randers Metrics ◽  
Naturally Reductive

AbstractIn this paper we study left invariant Einstein–Randers metrics on compact Lie groups. First, we give a method to construct left invariant non-Riemannian Einstein–Randers metrics on a compact Lie group, using the Zermelo navigation data. Then we prove that this gives a complete classification of left invariant Einstein–Randers metrics on compact simple Lie groups with the underlying Riemannian metric naturally reductive. Further, we completely determine the identity component of the group of isometries for this type of metrics on simple groups. Finally, we study some geometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvature of such metrics.

scholarly journals On the Balmer spectrum for compact Lie groups

2019 ◽  
Vol 156 (1) ◽  
pp. 39-76
Author(s):  
Tobias Barthel ◽  
J. P. C. Greenlees ◽  
Markus Hausmann
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Complete Classification ◽  
Prime Ideals ◽  
Compact Lie Group ◽  
Compact Lie Groups ◽  
Finite Set

We study the Balmer spectrum of the category of finite $G$-spectra for a compact Lie group $G$, extending the work for finite $G$ by Strickland, Balmer–Sanders, Barthel–Hausmann–Naumann–Nikolaus–Noel–Stapleton and others. We give a description of the underlying set of the spectrum and show that the Balmer topology is completely determined by the inclusions between the prime ideals and the topology on the space of closed subgroups of $G$. Using this, we obtain a complete description of this topology for all abelian compact Lie groups and consequently a complete classification of thick tensor ideals. For general compact Lie groups we obtain such a classification away from a finite set of primes $p$.

Geodesic orbit Randers metrics on spheres

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Shaoxiang Zhang ◽  
Zaili Yan
Keyword(s):  
Finsler Geometry ◽  
Riemannian Metrics ◽  
Complete Classification ◽  
Invariant Metrics ◽  
Navigation Data ◽  
Randers Metrics

AbstractStudying geodesic orbit Randers metrics on spheres, we obtain a complete classification of such metrics. Our method relies upon the classification of geodesic orbit Riemannian metrics on the spheres Sn in [17] and the navigation data in Finsler geometry. We also construct some explicit U(n + 1)-invariant metrics on S2n+1 and Sp(n + 1)U(1)-invariant metrics on S4n+3.

scholarly journals Non-naturally reductive Einstein metrics on normal homogeneous Einstein manifolds

2020 ◽  
pp. 2050079
Author(s):  
Zaili Yan ◽  
Shaoqiang Deng
Keyword(s):  
Lie Groups ◽  
Einstein Metrics ◽  
Complete Classification ◽  
Semisimple Lie Groups ◽  
Killing Form ◽  
Interesting Phenomenon ◽  
Product Metrics ◽  
Coset Spaces ◽  
Naturally Reductive

A quadruple of Lie groups [Formula: see text], where [Formula: see text] is a compact semisimple Lie group, [Formula: see text] are closed subgroups of [Formula: see text], and the related Casimir constants satisfy certain appropriate conditions, is called a basic quadruple. A basic quadruple is called Einstein if the Killing form metrics on the coset spaces [Formula: see text], [Formula: see text] and [Formula: see text] are all Einstein. In this paper, we first give a complete classification of the Einstein basic quadruples. We then show that, except for very few exceptions, given any quadruple [Formula: see text] in our list, we can produce new non-naturally reductive Einstein metrics on the coset space [Formula: see text], by scaling the Killing form metrics along the complement of [Formula: see text] in [Formula: see text] and along the complement of [Formula: see text] in [Formula: see text]. We also show that on some compact semisimple Lie groups, there exist a large number of left invariant non-naturally reductive Einstein metrics which are not product metrics. This discloses a new interesting phenomenon which has not been described in the literature.

Classification of 3-dimensional left-invariant almost paracontact metric structures

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Giovanni Calvaruso ◽  
Antonella Perrone
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Complete Classification ◽  
Natural Assumption ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Metric Structures

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

scholarly journals Unitary spherical representations of Drinfeld doubles

2018 ◽  
Vol 2018 (742) ◽  
pp. 157-186 ◽  
Author(s):  
Yuki Arano
Keyword(s):  
Quantum Group ◽  
Lie Group ◽  
Complete Classification ◽  
Unitary Representations ◽  
Compact Lie Group ◽  
Drinfeld Double ◽  
Quantum Analogue ◽  
Property T ◽  
Simply Connected

Abstract We study irreducible spherical unitary representations of the Drinfeld double of the q-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In the case of \mathrm{SU}_{q}(3) , we give a complete classification of such representations. As an application, we show the Drinfeld double of the quantum group \mathrm{SU}_{q}(2n+1) has property (T), which also implies central property (T) of the dual of \mathrm{SU}_{q}(2n+1) .

scholarly journals Algebraic Families of Harish-Chandra Pairs

2018 ◽  
Vol 2020 (15) ◽  
pp. 4776-4808 ◽  
Author(s):  
Joseph Bernstein ◽  
Nigel Higson ◽  
Eyal Subag
Keyword(s):  
Lie Groups ◽  
Reductive Group ◽  
Complete Classification ◽  
Compact Form ◽  
The Family

Abstract Mathematical physicists have studied degenerations of Lie groups and their representations, which they call contractions. In this paper we study these contractions, and also other families, within the framework of algebraic families of Harish-Chandra modules. We construct a family that incorporates both a real reductive group and its compact form, separate parts of which have been studied individually as contractions. We give a complete classification of generically irreducible families of Harish-Chandra modules in the case of the family associated to $SL(2,\mathbb{R})$.

A Bilinear Fractional Integral on Compact Lie Groups

2011 ◽  
Vol 54 (2) ◽  
pp. 207-216 ◽  
Author(s):  
Jiecheng Chen ◽  
Dashan Fan
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Fractional Integral ◽  
Compact Lie Group ◽  
Compact Lie Groups ◽  
Boundedness Property ◽  
Recent Theorem

AbstractAs an analog of a well-known theoremon the bilinear fractional integral on ℝn by Kenig and Stein, we establish the similar boundedness property for a bilinear fractional integral on a compact Lie group. Our result is also a generalization of our recent theorem about the bilinear fractional integral on torus.

scholarly journals A CLASSIFICATION OF THE STABLE TYPE OF BG∧p FOR COMPACT LIE GROUPS

Topology ◽  
1999 ◽  
Vol 38 (1) ◽  
pp. 1-21 ◽  
Author(s):  
John Martino ◽  
Stewart Priddy
Keyword(s):  
Lie Groups ◽  
Compact Lie Groups ◽  
Stable Type

scholarly journals Einstein metrics on compact Lie groups which are not naturally reductive

2011 ◽  
Vol 160 (1) ◽  
pp. 261-285 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
Kunihiko Mori ◽  
Yusuke Sakane
Keyword(s):  
Lie Groups ◽  
Einstein Metrics ◽  
Compact Lie Groups ◽  
Naturally Reductive
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