The aim is to show that a definable group in such fields must be closely related to the rational points of an algebraic group and to investigate the structure fixed pointwise by a generic automorphism
in a generic differential difference field.
Then is it true that for any KX-negative extremal ray R [subset] [bar.NE](X) of divisorial type, there exists a positive integer k such that [([f.sup.k]).sub.*](R) = R for the automorphism
[([f.sup.k]).sub.*] : [N.sub.1](X) [equivalent] [N.sub.1](X) induced from the k-th power [f.sup.k] = f [??] ...
The Nakayama automorphism
has not been studied explicitly for skew PBW extensions.
is a distinguished k-algebra automorphism
of a Frobenius algebra A which measures how far A is from being a symmetric algebra, where k is a fixed field.
(iii) The Dunkl transform f [right arrow] [??] is a topological automorphism
g--the inner automorphism
of G, generated by an element g [member of] G;
[[bar.f].sub.n] is a braid-like automorphism
of [F(k)/F[(k).sub.n]] that is (i) it sends the class of each generator [[alpha].sub.i] into a conjugate of itself and (ii) it sends the class of the product [[alpha].sub.1] [[alpha].sub.2] ...
We also give an explicit form of the automorphism
group of G(H, f).
Graph r is called a vertex-transitive graph, if, for any x, y [member of] V, there is some [pi] in Aut([GAMMA]), the automorphism
group of [bar.[GAMMA]], such that [pi](x) = y.
Bhutani  discussed automorphism
of fuzzy graphs.
In addition the group of all automorphisms
of a free group F, denoted by Aut(F) , is generated by a regular Nielsen transformation between two basis of F, and each regular Nielsen transformation between two basis of F defines an automorphism
of F, see (, Korollar 2.10).
Note that an automorphism
[phi] of a field F is a bijection [phi] : F [right arrow] F such that [phi](a + b) = [phi](a) + [phi](b) and [phi](ab) = [phi](a)[phi}(b) for all a, b [member of] F.