35 research outputs found
Remarks on a normal subgroup of GA_n
We show that the subgroup generated by locally finite polynomial
automorphisms of k^n is normal in GA_n. Also, some properties of normal
subgroups of GA_n containing all diagonal automorphisms are given.Comment: 5 page
Hamiltonian Formalism in Quantum Mechanics
Heisenberg motion equations in Quantum mechanics can be put into the Hamilton
form. The difference between the commutator and its principal part, the Poisson
bracket, can be accounted for exactly. Canonical transformations in Quantum
mechanics are not, or at least not what they appear to be; their properties are
formulated in a series of Conjectures
On the lifting of the Nagata automorphism
It is proved that the Nagata automorphism (Nagata coordinates, respectively)
of the polynomial algebra over a field cannot be lifted to a
-automorphism (-coordinate, respectively) of the free associative algebra
. The proof is based on the following two new results which have
their own interests: degree estimate of and tameness of
the automorphism group .Comment: 15 page
Affine modifications and affine hypersurfaces with a very transitive automorphism group
We study a kind of modification of an affine domain which produces another
affine domain. First appeared in passing in the basic paper of O. Zariski
(1942), it was further considered by E.D. Davis (1967). The first named author
applied its geometric counterpart to construct contractible smooth affine
varieties non-isomorphic to Euclidean spaces. Here we provide certain
conditions which guarantee preservation of the topology under a modification.
As an application, we show that the group of biregular automorphisms of the
affine hypersurface given by the equation
where acts transitively on the
smooth part reg of for any We present examples of such
hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction
Holomorphic automorphisms of Danielewski surfaces II -- structure of the overshear group
We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces
and investigate their group of holomorphic automorphisms. Our main result
states that the overshear group which is known to be dense in the identity
component of the holomorphic automorphism group, is a free amalgamated product.Comment: 24 page