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.

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 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 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 Twisted Weyl Groups of Compact Lie Groups and Nonabelian Cohomology

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 21
Author(s):  
Ming Liu ◽  
Xia Zhang
Keyword(s):  
Weyl Group ◽  
Lie Groups ◽  
Lie Group ◽  
Weyl Groups ◽  
Module Structure ◽  
Compact Lie Groups ◽  
Compact Torus ◽  
Nonabelian Cohomology ◽  
Connected Lie Group

Given a compact connected Lie group G with an S 1 -module structure and a maximal compact torus T of G S 1 , we define twisted Weyl group W ( G , S 1 , T ) of G associated to S 1 -module and show that two elements of T are δ -conjugate if and only if they are in one W ( G , S 1 , T ) -orbit. Based on this, we prove that the natural map W ( G , S 1 , T ) \ H 1 ( S 1 , T ) → H 1 ( S 1 , G ) is bijective, which reduces the calculation for the nonabelian cohomology H 1 ( S 1 , G ) .

scholarly journals Equivariant K-theory of compact Lie groups with involution

2014 ◽  
Vol 13 (2) ◽  
pp. 313-335
Author(s):  
Po Hu ◽  
Igor Kriz ◽  
Petr Somberg
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Compact Lie Groups ◽  
K Theory ◽  
Simply Connected

AbstractFor a compact simply connected simple Lie group G with an involution α, we compute the G ⋊ ℤ/2-equivariant K-theory of G where G acts by conjugation and ℤ/2 acts either by α or by g ↦ α(g)−1. We also give a representation-theoretic interpretation of those groups, as well as of KG(G).

Topological conjugacy of automorphism flows on compact Lie groups

2000 ◽  
Vol 20 (2) ◽  
pp. 335-342 ◽  
Author(s):  
SIDDHARTHA BHATTACHARYA
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Topological Conjugacy ◽  
Compact Lie Groups ◽  
Connected Lie Group

Let $G$ be a compact connected Lie group and ${\rm Aut}(G)$ be the group of Lie automorphisms of $G$. We describe a condition on $G$ under which topological conjugacy of the flows on $G$ induced by two one-parameter subgroups $\phi$ and $\psi$ of ${\rm Aut}(G)$ implies conjugacy of $\phi$ and $\psi$ in ${\rm Aut}(G)$. The condition is verified for $Sp(n)$, $SO(2n+1)$ and ${\rm Spin}(2n+1)$.

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 Homotopy Groups of Compact Lie Groups E6, E7 and E8

1968 ◽  
Vol 32 ◽  
pp. 109-139 ◽  
Author(s):  
Hideyuki Kachi
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Characteristic Zero ◽  
Exterior Algebra ◽  
Homotopy Groups ◽  
Compact Lie Groups ◽  
Simply Connected ◽  
Connected Lie Group

Let G be a simple, connected, compact and simply-connected Lie group. If k is the field with characteristic zero, then the algebra of cohomology H*(G ; k) is the exterior algebra generated by the elements x1, …, xl of the odd dimension n1, …, nl; the integer l is the rank of G and is the dimension of G.

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.

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