I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 3, PAGES 757-776
Roots in the universal covering group of the unimodular -matrix group
T. V. Dubrovina
N. I. Dubrovin
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The equation has been
solved in the universal covering group of the group
If is not
a central element, then the -th root
exists and is unique.
In the case when belongs to
the center of the universal covering , the set of
all solutions may be empty or may form a two-dimensional
submanifold of the manifold .
The following two questions are considered.
(A) How wide may be this submanifold from the algebraic
point of view? (B) How can we complete
the group with absent roots?
Of the results close to the main theorem one can mention
the following: the semigroup , consisting of all matrices with non-negative coefficients, is complete,
that is one can derive any root from any element.
All articles are
published in Russian.
Last modified: December 8, 2000