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 $p$.

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 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) .

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 Hyperkähler metrics associated to compact Lie groups

1996 ◽  
Vol 120 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Andrew Dancer ◽  
Andrew Swann
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Cotangent Bundle ◽  
Symplectic Structure ◽  
Compact Lie Group ◽  
Compact Lie Groups ◽  
Left And Right ◽  
Hyperkähler Metrics

It is well known that the cotangent bundle of any manifold has a canonical symplectic structure. If we specialize to the case when the manifold is a compact Lie group G, then this structure is preserved by the actions of G on T*G induced by left and right translation on G. We refer to these as the left and right actions of G on T*G.

scholarly journals Resolving actions of compact Lie groups

1978 ◽  
Vol 18 (2) ◽  
pp. 243-254 ◽  
Author(s):  
M.J. Field
Keyword(s):  
Lie Groups ◽  
Cyclic Group ◽  
Lie Group ◽  
Compact Lie Group ◽  
Compact Lie Groups ◽  
General Process ◽  
Orbit Types

A general process for the desingularization of smooth actions of compact Lie groups is described. If G is a compact Lie group, it is shown that there is naturally associated to any compact G manifold M a compact G × (Z/2)p manifold on which G acts principally. Here Z/2 denotes the cyclic group of order two and p + 1 is the number of orbit types of the G action on M.

scholarly journals The Pimsner-Voiculescu sequence for coactions of compact Lie groups

2012 ◽  
Vol 110 (2) ◽  
pp. 297
Author(s):  
Magnus Goffeng
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Compact Lie Group ◽  
Compact Lie Groups

The Pimsner-Voiculescu sequence is generalized to a Pimsner-Voiculescu tower describing the $KK$-category equivariant with respect to coactions of a compact Lie group satisfying the Hodgkin condition. A dual Pimsner-Voiculescu tower is used to show that coactions of a compact Hodgkin-Lie group satisfy the Baum-Connes property.

scholarly journals A classification of equivariant gerbe connections

2019 ◽  
Vol 21 (02) ◽  
pp. 1850001
Author(s):  
Byungdo Park ◽  
Corbett Redden
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Existence And Uniqueness ◽  
Smooth Manifold ◽  
Equivariant Cohomology ◽  
Compact Lie Group ◽  
Semisimple Lie Groups ◽  
Isomorphism Classes ◽  
Bundle Gerbe

Let [Formula: see text] be a compact Lie group acting on a smooth manifold [Formula: see text]. In this paper, we consider Meinrenken’s [Formula: see text]-equivariant bundle gerbe connections on [Formula: see text] as objects in a 2-groupoid. We prove this 2-category is equivalent to the 2-groupoid of gerbe connections on the differential quotient stack associated to [Formula: see text], and isomorphism classes of [Formula: see text]-equivariant gerbe connections are classified by degree 3 differential equivariant cohomology. Finally, we consider the existence and uniqueness of conjugation-equivariant gerbe connections on compact semisimple Lie groups.

ON THE PROBABILITY DISTRIBUTION OF THE PRODUCT OF POWERS OF ELEMENTS IN COMPACT LIE GROUPS

2019 ◽  
Vol 100 (3) ◽  
pp. 440-445
Author(s):  
VU THE KHOI
Keyword(s):  
Probability Distribution ◽  
Lie Groups ◽  
Infinite Series ◽  
Lie Group ◽  
Convergent Series ◽  
Compact Lie Group ◽  
Compact Lie Groups

In this paper, we study the probability distribution of the word map $w(x_{1},x_{2},\ldots ,x_{k})=x_{1}^{n_{1}}x_{2}^{n_{2}}\cdots x_{k}^{n_{k}}$ in a compact Lie group. We show that the probability distribution can be represented as an infinite series. Moreover, in the case of the Lie group $\text{SU}(2)$, our computations give a nice convergent series for the probability distribution.

scholarly journals S and g*λ-functions on compact Lie groups

1996 ◽  
Vol 61 (3) ◽  
pp. 327-344 ◽  
Author(s):  
Brian E. Blank ◽  
Dashan Fan
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Hardy Spaces ◽  
Compact Lie Group ◽  
Compact Lie Groups

AbstractWe characterize the Hardy spaces Hp(G) of a compact Lie groupG by means of S-functions in analogy with the theorem of Fefferman-Stein for Rn. We also characterize Hp(G) by means of the -functions.

Condition that All Irreducible Representations of a Compact Lie Group, if Restricted to a Subgroup, Contain no Representation More than Once

1972 ◽  
Vol 24 (3) ◽  
pp. 432-438 ◽  
Author(s):  
Fredric E. Goldrich ◽  
Eugene P. Wigner
Keyword(s):  
Irreducible Representation ◽  
Lie Groups ◽  
Finite Groups ◽  
Lie Group ◽  
Unitary Group ◽  
Unit Vector ◽  
Doctoral Dissertation ◽  
Irreducible Representations ◽  
Compact Lie Group ◽  
Compact Lie Groups

One of the results of the theory of the irreducible representations of the unitary group in n dimensions Un is that these representations, if restricted to the subgroup Un-1 leaving a vector (let us say the unit vector e1 along the first coordinate axis) invariant, do not contain any irreducible representation of this Un-1 more than once (see [1, Chapter X and Equation (10.21)]; the irreducible representations of the unitary group were first determined by I. Schur in his doctoral dissertation (Berlin, 1901)). Some time ago, a criterion for this situation was derived for finite groups [3] and the purpose of the present article is to prove the aforementioned result for compact Lie groups, and to apply it to the theory of the representations of Un.

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