Tame and wild coordinates and automorphisms
of polynomial and free associative algebras
Mr. Shengjun Gong
Abstract
Understanding automorphisms and coordinates are of the major topics in the
study of problems concerning polynomial algebras, such as the Jacobian Conjecture, Zariski's
Cancellation Problem, the Embedding Conjecture; also
the Tame Generator Problem, which I will concentrate in the talk.
Firstly, I will give some
results on tame and wild automorphisms of the
polynomial algebra R[x,y] where R is a Q-algebra. We also consider
the properties of the (tame or wild) coordinates, i.e., the images of x under the (tame or wild) automorphisms of R[x,y]. The case of the free
associative algebra is treated as well.
Extending to three
variables, I will introduce some results about the "tame generator
problem", including the (strong) Nagata Conjecture and (strnog) Anick Conjecture recently
solved by Dr. Yu and his colleagues. The emphasis lies in the methodologies
such as: Peak reduction; Degree estimatation; Parametrization (for coordinates), and (in the free
associative algebra case) Push-down to free metabelian
algebras; Defining relations for tame subgroups of the automorphism
groups.
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Room 517, Meng
Wah Complex, HKU |
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All are
welcome |
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