Canonical States on the Group of Automorphisms of a Homogeneous Tree

1996 ◽  
pp. 171-178
Author(s):  
G. Kuhn ◽  
A. Vershik
Keyword(s):  
Homogeneous Tree ◽  
Group Of Automorphisms

scholarly journals Trees and Reflection Groups

10.37236/1912 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Humberto Luiz Talpo ◽  
Marcelo Firer
Keyword(s):  
Fixed Points ◽  
Homogeneous Tree ◽  
Reflection Groups ◽  
Involutive Automorphism ◽  
Group Of Automorphisms ◽  
Topological Closure ◽  
Index 2

We define a reflection in a tree as an involutive automorphism whose set of fixed points is a geodesic and prove that, for the case of a homogeneous tree of degree $4k$, the topological closure of the group generated by reflections has index $2$ in the group of automorphisms of the tree.

scholarly journals A product formula for spherical representations of a group of automorphisms of a homogeneous tree, I

2000 ◽  
Vol 353 (1) ◽  
pp. 349-364 ◽  
Author(s):  
Donald I. Cartwright ◽  
Gabriella Kuhn ◽  
Paolo M. Soardi
Keyword(s):  
Product Formula ◽  
Homogeneous Tree ◽  
Group Of Automorphisms

scholarly journals Constructions for arc-transitive digraphs

1995 ◽  
Vol 59 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Marston Conder ◽  
Peter Lorimer ◽  
Cheryl Praeger
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Finite Groups ◽  
Transitive Permutation Group ◽  
Group Of Automorphisms ◽  
Representations Of Finite Groups ◽  
Regular Digraph

AbstractA number of constructions are given for arc-transitive digraphs, based on modifications of permutation representations of finite groups. In particular, it is shown that for every positive integer s and for any transitive permutation group p of degree k, there are infinitely many examples of a finite k-regular digraph with a group of automorphisms acting transitively on s-arcs (but not on (s + 1)-arcs), such that the stabilizer of a vertex induces the action of P on the out-neighbour set.

The group of automorphisms of a commutative algebra

1995 ◽  
Vol 219 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Francisco Guil-Asensio ◽  
Manuel Saorín
Keyword(s):  
Commutative Algebra ◽  
Group Of Automorphisms

scholarly journals A note on the fixed subring of an FPF ring

1989 ◽  
Vol 40 (1) ◽  
pp. 109-111 ◽  
Author(s):  
John Clark
Keyword(s):  
Finite Group ◽  
Associative Ring ◽  
Finitely Generated ◽  
Group Of Automorphisms ◽  
Direct Sum ◽  
Epimorphic Image ◽  
A Finite Group

An associative ring R with identity is called a left (right) FPF ring if given any finitely generated faithful left (right) R-module A and any left (right) R-module M then M is the epimorphic image of a direct sum of copies of A. Faith and Page have asked if the subring of elements fixed by a finite group of automorphisms of an FPF ring need also be FPF. Here we present examples showing the answer to be negative in general.

The spread of the potential on a homogeneous tree

1998 ◽  
Vol 175 (1) ◽  
pp. 29-57 ◽  
Author(s):  
Carla Cattaneo
Keyword(s):  
Homogeneous Tree
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