Relation Modules for Conjugate Algebraic Numbers

The present project deals with problems from the theory of algebraic equations which can be considered as classical: (polynomial) relations between the solutions of such an equation. Questions of this type date back to Evariste Galois (1811-1831), who developed the theory named after him, a cornerstones of modern algebra. For instance, one of Galois` most famous results connects the solvability of an important class of algebraic equations with the existence of a special type of relations. The contributors to this project work with modern theoretical tools like representation theory and algebraic number theory and investigate, first of all and to a far reaching extent, linear relations, but also relations of a higher degree. These investigations are based on fundamental results of their own combined with clever methods of other researchers. One important aim will be the construction of explicit examples who actually behave like the theory predicts. For this purpose computer algebra systems together with software packages developed by the authors are being used. Besides examples of this kind, theoretical aims play a major role, for instance, a more thorough investigation of "wild" linear relations, whose mathematical nature is far from being well understood.

The present project deals with problems from the theory of algebraic equations which can be considered as classical: (polynomial) relations between the solutions of such an equation. Questions of this type date back to Evariste Galois (1811-1831), who developed the theory named after him, a cornerstones of modern algebra. For instance, one of Galois` most famous results connects the solvability of an important class of algebraic equations with the existence of a special type of relations. The contributors to this project work with modern theoretical tools like representation theory and algebraic number theory and investigate, first of all and to a far reaching extent, linear relations, but also relations of a higher degree. These investigations are based on fundamental results of their own combined with clever methods of other researchers. One important aim will be the construction of explicit examples who actually behave like the theory predicts. For this purpose computer algebra systems together with software packages developed by the authors are being used. Besides examples of this kind, theoretical aims play a major role, for instance, a more thorough investigation of "wild" linear relations, whose mathematical nature is far from being well understood.