scholarly journals Proper affine actions in non-swinging representations

2018 ◽  
Vol 12 (2) ◽  
pp. 449-528 ◽  
Author(s):  
Ilia Smilga
Keyword(s):  
Affine Actions

Affine Actions of Uq(sl(2)) on Polynomial Rings

2015 ◽  
Vol 58 (2) ◽  
pp. 233-240
Author(s):  
Jeffrey Bergen
Keyword(s):  
Polynomial Ring ◽  
Scalar Multiplication ◽  
Polynomial Rings ◽  
Affine Actions

AbstractWe classify the affine actions of Uq(sl(2)) on commutative polynomial rings in m ≥ 1 variables. We show that, up to scalar multiplication, there are two possible actions. In addition, for each action, the subring of invariants is a polynomial ring in either m or m−1 variables, depending upon whether q is or is not a root of 1.

scholarly journals Translations in simply transitive affine actions of Heisenberg type Lie groups

2003 ◽  
Vol 359 (1-3) ◽  
pp. 101-111 ◽  
Author(s):  
Tine De Cat ◽  
Karel Dekimpe ◽  
Paul Igodt
Keyword(s):  
Lie Groups ◽  
Heisenberg Type ◽  
Transitive Affine ◽  
Affine Actions

scholarly journals K-theory of affine actions

2019 ◽  
Vol 301 (2) ◽  
pp. 639-666
Author(s):  
James Waldron
Keyword(s):  
K Theory ◽  
Affine Actions

scholarly journals AFFINE ACTIONS ON NON-ARCHIMEDEAN TREES

2013 ◽  
Vol 23 (02) ◽  
pp. 217-253 ◽  
Author(s):  
SHANE O. ROURKE
Keyword(s):  
Abelian Group ◽  
Heisenberg Group ◽  
Isometric Action ◽  
Length Functions ◽  
Common Generalization ◽  
New Class ◽  
Discrete Heisenberg Group ◽  
Affine Action ◽  
Affine Actions

We initiate the study of affine actions of groups on Λ-trees for a general ordered abelian group Λ; these are actions by dilations rather than isometries. This gives a common generalization of isometric action on a Λ-tree, and affine action on an ℝ-tree as studied by Liousse. The duality between based length functions and actions on Λ-trees is generalized to this setting. We are led to consider a new class of groups: those that admit a free affine action on a Λ-tree for some Λ. Examples of such groups are presented, including soluble Baumslag–Solitar groups and the discrete Heisenberg group.

scholarly journals Cohomology of deformations

2014 ◽  
Vol 07 (01) ◽  
pp. 81-104 ◽  
Author(s):  
Uri Bader ◽  
Piotr W. Nowak
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Linear Part ◽  
Quantitative Estimates ◽  
Fixed Point Properties ◽  
Vanishing Of Cohomology ◽  
Uniformly Bounded ◽  
Affine Actions

In this paper we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As applications we obtain deformation theorems for fixed point properties on Banach spaces. In particular, our results yield fixed point theorems for affine actions in which the linear part is not uniformly bounded. Our proofs are effective and allow for quantitative estimates.

scholarly journals Affine actions of a free semigroup on the real line

2006 ◽  
Vol 26 (05) ◽  
pp. 1285 ◽  
Author(s):  
VITALY BERGELSON ◽  
MICHAL MISIUREWICZ ◽  
SAMUEL SENTI
Keyword(s):  
Real Line ◽  
Free Semigroup ◽  
The Real ◽  
Affine Actions

scholarly journals Local rigidity of affine actions of higher rank groups and lattices

2009 ◽  
Vol 170 (1) ◽  
pp. 67-122 ◽  
Author(s):  
David Fisher ◽  
Gregory Margulis
Keyword(s):  
Local Rigidity ◽  
Higher Rank ◽  
Affine Actions

AN ARITHMETICAL INVARIANT OF ORBITS OF AFFINE ACTIONS AND ITS APPLICATION TO SIMILARITY CLASSES OF QUADRATIC SPACES

2010 ◽  
Vol 06 (06) ◽  
pp. 1215-1253
Author(s):  
ANTHONY C. KABLE
Keyword(s):  
Automorphism Group ◽  
Algebraic Group ◽  
Number Field ◽  
General Framework ◽  
Class Group ◽  
Regular Function ◽  
Affine Variety ◽  
Natural Parameter ◽  
Ring Of Integers ◽  
Affine Actions

Given an action of an affine algebraic group on an affine variety and a relatively invariant regular function, all defined over the ring of integers of a number field and having suitable additional properties, an invariant of the rational orbits of the action is defined. This invariant, the reduced replete Steinitz class, takes its values in the reduced replete class group of the number field. The general framework is then applied to obtain an invariant of similarity classes of non-degenerate quadratic spaces of even rank. The invariant is related to more familiar invariants. It is shown that if the similarity classes are weighted by the volume of an associated automorphism group then their reduced replete Steinitz classes are asymptotically uniformly distributed with respect to a natural parameter.

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