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.

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 $p$.

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.

Unstable homotopy classification of

1996 ◽  
Vol 119 (1) ◽  
pp. 119-137 ◽  
Author(s):  
John Martino ◽  
Stewart Priddy
Keyword(s):  
Lie Group ◽  
Compact Lie Group ◽  
Classifying Space ◽  
Homotopy Classification ◽  
Completion Process

For nilpotent spaces p-completion is well behaved and reasonably well understood. By p–completion we mean Bousfield–Kan completion with respect to the field Fp [BK]. For non-nilpotent spaces the completion process often has a chaotic effect, this is true even for small spaces. One knows, however, that the classifying space of a compact Lie group is Fp-good even though it is usually non-nilpotent.

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 Extension theorems for smooth functions on real analytic spaces and quotients by Lie groups and smooth stability

1977 ◽  
Vol 24 (4) ◽  
pp. 440-457
Author(s):  
G. S. Wells
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Analytic Space ◽  
Main Step ◽  
Compact Lie Group ◽  
Orbit Type ◽  
Smooth Functions ◽  
Extension Theorems ◽  
Real Analytic

AbstractExtension theorems are proved for smooth functions on a coherent real analytic space for which local defining functions exist which are finitely determined in the sense of J. Mather, (1968), and for smooth functions invariant under the action of a compact lie groupG. thus providing the main step in the proof that smooth infinitesimal stability implies smooth stability in the appropriate categories. In addition the remaining step for the category ofCxG-manifolds of finite orbit type is filled in.

scholarly journals Some remarks on invariant Poisson quasi-Nijenhuis structures on Lie groups

2019 ◽  
Vol 16 (07) ◽  
pp. 1950097
Author(s):  
Ghorbanali Haghighatdoost ◽  
Zohreh Ravanpak ◽  
Adel Rezaei-Aghdam
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Lie Group ◽  
Baxter Equation ◽  
Complex Structures ◽  
Lie Bialgebra ◽  
Text Structures ◽  
Generalized Complex Structures ◽  
Generalized Complex

We study right-invariant (respectively, left-invariant) Poisson quasi-Nijenhuis structures on a Lie group [Formula: see text] and introduce their infinitesimal counterpart, the so-called r-qn structures on the corresponding Lie algebra [Formula: see text]. We investigate the procedure of the classification of such structures on the Lie algebras and then for clarity of our results we classify, up to a natural equivalence, all [Formula: see text]-[Formula: see text] structures on two types of four-dimensional real Lie algebras. We mention some remarks on the relation between [Formula: see text]-[Formula: see text] structures and the generalized complex structures on the Lie algebras [Formula: see text] and also the solutions of modified Yang–Baxter equation (MYBE) on the double of Lie bialgebra [Formula: see text]. The results are applied to some relevant examples.

scholarly journals Pro-Lie groups which are infinite-dimensional Lie groups

2009 ◽  
Vol 146 (2) ◽  
pp. 351-378 ◽  
Author(s):  
K. H. HOFMANN ◽  
K.-H. NEEB
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Exponential Function ◽  
Lie Group ◽  
Smooth Manifold ◽  
Projective Limit ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Infinite Dimensional Lie Groups

AbstractA pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this paper we show that a pro-Lie group G is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operations are smooth if and only if G is locally contractible. We also characterize the corresponding pro-Lie algebras in various ways. Furthermore, we characterize those pro-Lie groups which are locally exponential, that is, they are Lie groups with a smooth exponential function which maps a zero neighbourhood in the Lie algebra diffeomorphically onto an open identity neighbourhood of the group.

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