EAN: 9783662553480

ALGEBRAIC THEORY OF LOCALLY NILPOTENT DERIVATIO...

This book explores the theory and application of locally nilpotent derivations  a subject
motivated by questions in affine algebraic geometry and having fundamental connections to areas
such as commutative algebra  representation theory  Lie algebras and differential equations.
The author provides a unified treatment of the subject  beginning with 16 First Principles on
which the theory is based. These are used to establish classical results  such as Rentschler's
Theorem for the plane and the Cancellation Theorem for Curves. More recent results  such as
Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings  are also
discussed. Topics of special interest include progress in classifying additive actions on
three-dimensional affine space  finiteness questions (Hilbert's 14th Problem)  algorithms  the
Makar-Limanov invariant  and connections to the Cancellation Problem and the Embedding Problem.
A lot of new material is included in this expanded second edition  such as canonical
factorization of quotient morphisms  and a more extended treatment of linear actions. The
reader will also find a wealth of examples and open problems and an updated resource for future
investigations.

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