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Computation with linear algebraic groups / Willem Adriaan de Graaf

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Monographs and Research Notes in MathematicsPublisher: Boca Raton, London, New York : CRC Press, [2017]Edition: First editionDescription: 1 Online-RessourceISBN:
  • 9781351646451
  • 9781315120140
Subject(s): Additional physical formats: 9781498722919 | 9781351636933 | 9781498722902. | Erscheint auch als: Computation with linear algebraic groups. Druck-Ausgabe Boca Raton, London, New York : CRC Press, Taylor & Francis Group, 2017. xiv, 327 pagesLOC classification:
  • QA179
Online resources: Summary: 2.6.2 Cartan's criterion for solvability2.6.3 Computing the solvable radical; 2.6.4 Finding a non-nilpotent element; 2.6.5 Computing the nilradical; 2.7 Semisimple Lie algebras; 2.7.1 Derivations and the Jordan decomposition; 2.7.2 Levi's theorem; 2.8 Root systems; 2.8.1 Cartan matrices; 2.8.2 Root systems; 2.8.3 The Weyl group; 2.9 Classification of simple Lie algebras; 2.9.1 Representations of sl(2, k); 2.9.2 From Lie algebra to root system; 2.9.3 Canonical generators and isomorphisms; 2.9.4 Structure constants of semisimple Lie algebras; 2.10 Universal enveloping algebrasSummary: 2.10.1 Poincare-B́irkhoff-Witt theorem2.10.2 Left ideals of universal enveloping algebras; 2.10.3 Integral forms; 2.11 Representations of semisimple Lie algebras; 2.11.1 Highest weight modules; 2.11.2 Classification of irreducible modules; 2.11.3 Path model; 2.11.4 Constructing irreducible modules; 2.12 Reductive Lie algebras; 2.13 The Jacobson-Morozov theorem; 2.14 Notes; Chapter 3 Linear Algebraic Groups: Basic Constructions; 3.1 Definition and first properties; 3.2 Connected components; 3.3 Semidirect products; 3.4 The Lie algebra of an algebraic group; 3.5 Subgroups and subalgebrasSummary: "Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms.Computation with Linear Algebraic Groups offers an invaluable guide to graduate students and researchers working in algebraic groups, computational algebraic geometry, and computational group theory, as well as those looking for a concise introduction to the theory of linear algebraic groups."--Provided by publisherPPN: PPN: 1003038131Package identifier: Produktsigel: ZDB-4-NLEBK
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