Abstract:
It has long noticed the analogy between affine algebraic groups and
the Cremona groups. One of the main elements of the structural theory
of affine
algebraic groups are Borel subgroups. Their key feature is
conjugation. The concept of a Borel subgroup makes sense
for the Cremona groups as well. This naturally leads to attempts to
understand their role in the
theory of these groups, in particular, to explore the problem of their
conjugation.
The first results in this direction was obtained by H. Bass in 1984.
Now we know
more on this topic. I shall tell about the results, known to me, on
this range of issues.
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