1,359 research outputs found
Cyclic metric Lie groups
Cyclic metric Lie groups are Lie groups equipped with a left-invariant metric
which is in some way far from being biinvariant, in a sense made explicit in
terms of Tricerri and Vanhecke's homogeneous structures. The semisimple and
solvable cases are studied. We extend to the general case, Kowalski-Tricerri's
and Bieszk's classifications of connected and simply-connected unimodular
cyclic metric Lie groups for dimensions less than or equal to five
Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids; Higher dimensions
This paper illustrates the themes of the title in terms of: van Kampen type
theorems for the fundamental groupoid; holonomy and monodromy groupoids; and
higher homotopy groupoids. Interaction with work of the writer is explored.Comment: 13 pages; Expansion of an invited talk given to the 7th Conference on
the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles
Ehresmann, Bedlewo 8.05.2005-15.05.2005 (Poland) Version 2: corrections of a
date and some grammar, slight referencing changes, and a small comment added
Version4. Theorem 2.2 got corrected and then uncorrected! It is now
corrected. Version5. Reference added. Various minor improvements made in
reaction to comment
Isomorphism in expanding families of indistinguishable groups
For every odd prime and every integer there is a Heisenberg
group of order that has pairwise
nonisomorphic quotients of order . Yet, these quotients are virtually
indistinguishable. They have isomorphic character tables, every conjugacy class
of a non-central element has the same size, and every element has order at most
. They are also directly and centrally indecomposable and of the same
indecomposability type. The recognized portions of their automorphism groups
are isomorphic, represented isomorphically on their abelianizations, and of
small index in their full automorphism groups. Nevertheless, there is a
polynomial-time algorithm to test for isomorphisms between these groups.Comment: 28 page
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