Vanishing of the first-order cohomology on Olshanski spherical pairs

2021 ◽  
pp. 2150030
Author(s):  
Marouane Rabaoui
Keyword(s):  
Direct Limit ◽  
Unitary Representations ◽  
Limit Groups ◽  
First Order ◽  
Cohomology Space ◽  
Invariant Vectors

In this paper, we study the first-order cohomology space of countable direct limit groups related to Olshanski spherical pairs, relatively to unitary representations which do not have almost invariant vectors. In particular, we prove a variant of Delorme’s vanishing result of the first-order cohomology space for spherical representations of Olshanski spherical pairs.

scholarly journals EQUIVARIANT COMPRESSION OF CERTAIN DIRECT LIMIT GROUPS AND AMALGAMATED FREE PRODUCTS

2016 ◽  
Vol 58 (3) ◽  
pp. 739-752
Author(s):  
CHRIS CAVE ◽  
DENNIS DREESEN
Keyword(s):  
Finite Index ◽  
Direct Limit ◽  
Free Products ◽  
Limit Groups ◽  
Amalgamated Free Products

AbstractWe give a means of estimating the equivariant compression of a group G in terms of properties of open subgroups Gi ⊂ G whose direct limit is G. Quantifying a result by Gal, we also study the behaviour of the equivariant compression under amalgamated free products G1∗HG2 where H is of finite index in both G1 and G2.

scholarly journals Metric groups, unitary representations and continuous logic

2021 ◽  
Vol 29 (1) ◽  
pp. 35-48
Author(s):  
Aleksander Ivanov
Keyword(s):  
Unitary Representations ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Continuous Logic ◽  
Locally Compact ◽  
First Order ◽  
Property T ◽  
Metric Groups

Abstract We describe how properties of metric groups and of unitary representations of metric groups can be presented in continuous logic. In particular we find Lω 1 ω -axiomatization of amenability. We also show that in the case of locally compact groups some uniform version of the negation of Kazhdan’s property (T) can be viewed as a union of first-order axiomatizable classes. We will see when these properties are preserved under taking elementary substructures.

Differentiable structure for direct limit groups

1991 ◽  
Vol 23 (2) ◽  
pp. 99-109 ◽  
Author(s):  
Loki Natarajan ◽  
Enriqueta Rodr�guez-Carrington ◽  
Joseph A. Wolf
Keyword(s):  
Direct Limit ◽  
Differentiable Structure ◽  
Limit Groups

scholarly journals Direct limit groups and the Keesling-Mardešić shape fibration

1980 ◽  
Vol 86 (2) ◽  
pp. 471-476 ◽  
Author(s):  
Kenneth Goodearl ◽  
Thomas Rushing
Keyword(s):  
Direct Limit ◽  
Limit Groups

scholarly journals Direct limit groups do not have small subgroups

2007 ◽  
Vol 154 (6) ◽  
pp. 1126-1133 ◽  
Author(s):  
Helge Glöckner
Keyword(s):  
Direct Limit ◽  
Limit Groups

scholarly journals The Bott–Borel–Weil Theorem for direct limit groups

2001 ◽  
Vol 353 (11) ◽  
pp. 4583-4622 ◽  
Author(s):  
Loki Natarajan ◽  
Enriqueta Rodríguez-Carrington ◽  
Joseph A. Wolf
Keyword(s):  
Direct Limit ◽  
Limit Groups ◽  
Weil Theorem

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

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