Combinatorial methods: free groups, polynomials, and free algebras

The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20thCentury. INDICE: Preface.- Introduction.- I. Groups: Introduction. Classical Techniques. Test Elements. Other Special Elements. Automorphic Orbits.- II. Polynomial Algebras: Introduction. The Jacobian Conjecture. The Cancellation Conjecture. Nagata's Problem. The Embedding Problem. Coordinate Polynomials. Test Polynomials.- III. Free Nielsen-Schreier Algebras: Introduction. Schreier Varietiesof Algebras. Rank Theorems and Primitive Elements. Generalized Primitive Elements. Free Leibniz Algebras.- References.- Notations.- Author Index.- Subject Index.

• ISBN: 978-1-4419-2344-8
• Editorial: Springer
• Encuadernacion: Rústica
• Fecha Publicación: 14/03/2012
• Nº Volúmenes: 1
• Idioma: Inglés