Multiplicative Invariant Theory
By: Lorenz, Martin [author.].
Contributor(s): SpringerLink (Online service).
Material type:
BookSeries: Encyclopaedia of Mathematical Sciences: 135Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.Description: XII, 180 p. 5 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540273585.Subject(s): Mathematics | Algebra | Algebraic geometry | Mathematics | Algebra | Algebraic GeometryDDC classification: 512 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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E books
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PK Kelkar Library, IIT Kanpur | Available | EBK6428 |
Notations and Conventions -- Groups Acting on Lattices -- Permutation Lattices and Flasque Equivalence -- Multiplicative Actions -- Class Group -- Picard Group -- Multiplicative Invariants of Reflection Groups -- Regularity -- The Cohen-Macaulay Property -- Multiplicative Invariant Fields -- Problems.
Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori. Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2. The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.
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