Bøger af Alexander Zimmermann

This is the fi rst textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of fi nite groups. Character theory is developed in a highly pedagogical way including many examples and exercises covering at once the fi rst defi nitions up to Clifford theory, Brauer's induction theorem and the splitting fi eld theorem, as well as self-dual simple modules allowing bilinear forms. This latter part is done step by step using the approach given by Sin and Willems. Dirichlet characters and Dirichlet's result on primes in arithmetic progressions are given as an application. Examples of integral representations of fi nite groups are already detailed at a quite early stage where appropriate, so that the more systematic treatment of lattices over orders is natural. After that, the necessary number theory and homological algebra is developed as far as needed. Maximal as well as hereditary orders are introduced and the Auslander- Buchsbaum theorem is proved. The Jordan-Zassenhaus theorem on the fi niteness of lattices in a given vector space is fully proved. Then the development and properties of class groups of orders is a fi rst focus. As a further highlight Swan's example of a stably free but not free ideal over the integral group ring of the generalised quaternion group of order 32 is developed in great detail. A student friendly introduction to ordinary representation theory Many examples and exercises, including solutions for some of them, make the book well suited for self-study Leads coherently from ordinary character theory to the integral representation theory of lattices over orders Several topics appear for the fi rst time in a textbook, such as Sin-Willems' approach to self-dual simple modules and Swan's example of a stably free non free ideal.

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory.

Die Bedeutung der strategischen Planung nimmt in dem Maße zu, wie Unternehmen durch Fusionen, Zu- und Verkäufe komplexer werden. Heute versammeln nicht nur Großunternehmen, sondern zunehmend auch Mittelständler 30 ¿ 150 eigenständige Geschäftseinheiten unter einem Dach. Um unter diesen Bedingungen eine Gesamtstrategie zu erarbeiten, wurde eine Strategieplattform entwickelt, die von namhaften Unternehmen wie Siemens eingesetzt wird. Die Autoren stellen das strategische Informationssystem in mehreren Best-Practice-Beispielen anwenderorientiert vor.

Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broue's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure".