Jerzy Weyman – författare
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3 produkter
3 produkter
Del 149 - Cambridge Tracts in Mathematics
Cohomology of Vector Bundles and Syzygies
Inbunden, Engelska, 2003
1 837 kr
Skickas inom 7-10 vardagar
The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.
Häftad, Engelska, 2026
675 kr
Kommande
This book presents an accessible approach to an emerging theory of picture groups. Intended for graduate students and researchers, it explains the connections between several branches of algebra and topology, and demonstrates how they interact. It begins with foundational material on modulated quivers and their representations, cluster categories, and semi-invariants. The text then develops virtual analogues of classical results, allowing dimension vectors with negative coordinates. Finally, it defines the notion of a picture group associated to a semi-invariant picture, also introducing picture spaces which are CW-complexes constructed from semi-invariant pictures. For quivers of type $A_n$ the key theorem draws on K-theory and states that the associated picture space is a $K(G(A_n) , 1)$ connected CW-complex for the corresponding group $G(A_n)$ associated with the same quiver.
Inbunden, Engelska, 2018
1 568 kr
Skickas inom 5-8 vardagar
This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories.The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout the text. The book will also be of use to experts in such areas as representation theory, invariant theory and algebraic geometry, who want learn about application of quiver representations to their fields.