Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.
You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.
After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.
This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations.
The author provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings.
Topics of special interest include: progress in the dimension three case, finiteness questions (Hilbert’s 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. The reader will also find a wealth of pertinent examples and open problems and an up-to-date resource for research.
Content Level »Research
Keywords »Dimension - additive group action on affine varieties - algebra - algebraic geometry - commutative algebra - invariant theory - locally nilpotent derivation
First Principles.- Further Properties of Locally Nilpotent Derivations.- Polynomial Rings.- Dimension Two.- Dimension Three.- Linear Actions of Unipotent Groups.- Non-Finitely Generated Kernels.- Algorithms.- The Makar-Limanov and Derksen Invariants.- Slices, Embeddings and Cancellation.- Epilogue.