| Combinatorial Methods: Free Groups, Polynomials, and Free Algebras Softcover Repri Edition Contributor(s): Shpilrain, Vladimir (Author), Mikhalev, Alexander (Author), Yu, Jie-Tai (Author) |
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ISBN: 1441923446 ISBN-13: 9781441923448 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Geometry - Algebraic - Mathematics | Algebra - Abstract |
| Dewey: 512.2 |
| Series: CMS Books in Mathematics |
| Physical Information: 0.69" H x 6.14" W x 9.21" (1.01 lbs) 315 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book is about three seemingly independent areas of mathematics: combinatorial group theory, the theory of Lie algebras and affine algebraic geometry. Indeed, for many years these areas were being developed fairly independently. Combinatorial group theory, the oldest of the three, was born in the beginning of the 20th century as a branch of low-dimensional topology. Very soon, it became an important area of mathematics with its own powerful techniques. In the 1950s, combinatorial group theory started to influence, rather substantially, the theory of Lie algebrasj thus combinatorial theory of Lie algebras was shaped, although the origins of the theory can be traced back to the 1930s. In the 1960s, B. Buchberger introduced what is now known as Gr bner bases. This marked the beginning of a new, "combinatorial", era in commu- tative algebra. It is not very likely that Buchberger was directly influenced by ideas from combinatorial group theory, but his famous algorithm bears resemblance to Nielsen's method, although in a more sophisticated form. |