Alexander Zimmermann

This is the first textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of finite groups. After the introduction to simple modules allowing a non degenerate invariant bilinear form in any characteristic the author illustrates step by step the approach given by Sin and Willems. Dirichlet characters and results on primes in arithmetic progressions are given as applications.

From Ordinary to Integral Representation Theory

Characters of Groups and Lattices over Orders

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. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.

A Homological Algebra Point of View

Representation Theory

Steffen König

A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué'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". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.

Derived Equivalences for Group Rings

Carsten Linz

Günter Müller-Stewens

Many companies are relying on a business model that is fundamentally suited to a different era. Now, organizations are under pressure from new trends such as digitization and servitization. Trying to adapt to a new environment, they risk relying on improvements that only scratch the surface of developing a radically different value proposition. Based on rigorous research into companies that have successfully and radically redesigned their business models, Radical Business Model Transformation shows why they made the leap, what they had to do to achieve it and how it has transformed the potential for their organizations. This book is a step-by-step guide for leaders who want to seize the opportunity of new business models and gain a competitive advantage. It explains how to assess the status quo, identify the value of future business models and develop a transformation path. It also provides advice on how to involve both the leadership team and all other employees in order to implement successful business model transformation. Illustrative case studies of organizations that have crossed the line to a more transformative business range from exponential-growth companies like Netflix and global players like Xerox, SAP and Daimler to mid-sized hidden champions like Knorr-Bremse and LEGIC. Radical Business Model Transformation is essential reading for business leaders, transformation experts and MBA students interested in ensuring that their business model is future-proof and can withstand the new proliferation of innovations that are set to transform the business landscape.

Alexander Zimmermann

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