AFFINE ACTIONS ON NON-ARCHIMEDEAN TREES
2013 ◽
Vol 23
(02)
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pp. 217-253
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Keyword(s):
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.
2016 ◽
Vol 26
(07)
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pp. 1283-1321
Keyword(s):
1990 ◽
Vol 60
(1)
◽
pp. 195-203
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1995 ◽
Vol 58
(3)
◽
pp. 387-403
Keyword(s):
2019 ◽
Vol 22
(6)
◽
pp. 973-981
2018 ◽
Vol 61
(1)
◽
pp. 295-304
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Keyword(s):
2015 ◽
Vol 70
(4)
◽
pp. 657-714
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2014 ◽
Vol 8
◽
pp. 317-327
2019 ◽
Vol 18
(04)
◽
pp. 1950066
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Keyword(s):
1988 ◽
Vol 40
(04)
◽
pp. 833-864
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