Multiplicative invariant theory

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. TOC:Introduction.- Notations and Conventions.- List of Abbreviations and Symbols.- 1 Groups Acting on Lattices.- 2 Permutation Lattices and Flasque Equivalence.- 3 Multiplicative Actions.- 4 Class Group.- 5 Picard Group.- 6 Multiplicative Invariants of Reflection Groups.- 7 Regularity.- 8 The Cohen-Macaulay Property.- 9 Multiplicative Invariant Fields.- 10 Problems.- References

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• ISBN: 9783540243236 ; 3540243232
• Maße: 24 cm
• Umfang: 177 S.
• Sprache: Englisch
• Anmerkungen: Literaturverz. S. 161 - 171

Verweise und Beziehungen

• Erschienen in: Encyclopaedia of mathematical sciences ; 6[...]

Klassifikation und Themen

• Klassifikation: Mathematik
• Schlagwort: Invariantentheorie

Beteiligte, Orts- und Zeitangaben

• Ereignis: Veröffentlichung
• (wo): Berlin, Heidelberg, New York
• (wer): Springer
• (wann): 2005
• Urheber: Lorenz, Martin

Weitere Informationen

• Inhaltsverzeichnis: https://d-nb.info/973262591/04
• Rechteinformation: Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
• Letzte Aktualisierung: 11.06.2025, 14:26 MESZ