Algebraic Q-groups as Abstract Groups
Author | : Olivier Frécon |
Publisher | : |
Total Pages | : 99 |
Release | : 2018 |
Genre | : Algebra |
ISBN | : 9781470448158 |
Download Algebraic Q-groups as Abstract Groups Book in PDF, ePub and Kindle
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Algebraic Q Groups As Abstract Groups PDF full book. Access full book title Algebraic Q Groups As Abstract Groups.
Author | : Olivier Frécon |
Publisher | : |
Total Pages | : 99 |
Release | : 2018 |
Genre | : Algebra |
ISBN | : 9781470448158 |
Author | : Olivier Frécon |
Publisher | : American Mathematical Soc. |
Total Pages | : 99 |
Release | : 2018-10-03 |
Genre | : |
ISBN | : 1470429233 |
The author analyzes the abstract structure of algebraic groups over an algebraically closed field . For of characteristic zero and a given connected affine algebraic Q -group, the main theorem describes all the affine algebraic Q -groups such that the groups and are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic Q -groups and , the elementary equivalence of the pure groups and implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited.
Author | : Jens Carsten Jantzen |
Publisher | : American Mathematical Soc. |
Total Pages | : 594 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082184377X |
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author | : Vladimir Platonov |
Publisher | : Academic Press |
Total Pages | : 614 |
Release | : 1993-12-07 |
Genre | : Mathematics |
ISBN | : 9780080874593 |
This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.
Author | : J. S. Milne |
Publisher | : Cambridge University Press |
Total Pages | : 665 |
Release | : 2017-09-21 |
Genre | : Mathematics |
ISBN | : 1107167485 |
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author | : Thomas Q. Sibley |
Publisher | : American Mathematical Soc. |
Total Pages | : 478 |
Release | : 2021-06-08 |
Genre | : Education |
ISBN | : 1470460300 |
Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout. The book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester- or year-long algebra course.
Author | : Vladimir Platonov |
Publisher | : Cambridge University Press |
Total Pages | : 379 |
Release | : 2023-08-31 |
Genre | : Mathematics |
ISBN | : 052111361X |
The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.
Author | : Benjamin Fine |
Publisher | : JHU Press |
Total Pages | : 583 |
Release | : 2014-07-01 |
Genre | : Mathematics |
ISBN | : 1421411776 |
A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic
Author | : Daniel G. Coronell |
Publisher | : CRC Press |
Total Pages | : 693 |
Release | : 2015-10-15 |
Genre | : Science |
ISBN | : 1584885157 |
Introduction to MATLAB with Applications for Chemical and Mechanical Engineers provides applications from chemical engineering and biotechnology, such as thermodynamics, heat transfer, fluid mechanics, and mass transfer. The book features a section on input, output, and storage of data as well as a section on data analysis and parameter estimation that contains statistical analysis, curve fitting optimization, and error analysis. Many applied case studies are included from the engineering disciplines. It also offers instruction on the use of the MATLAB® optimization toolbox. With a CD-ROM of MATLAB programs, this text is essential for chemical engineers, mechanical engineers, applied mathematicians, and students.
Author | : Vladimir Platonov |
Publisher | : Cambridge University Press |
Total Pages | : 380 |
Release | : 2023-08-31 |
Genre | : Mathematics |
ISBN | : 1009380656 |
The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.