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Two-Dimensional Tame and Maximal Orders of Finite Representation Type

Two-Dimensional Tame and Maximal Orders of Finite Representation Type
Author: Idun Reiten
Publisher: American Mathematical Soc.
Total Pages: 85
Release: 1989
Genre: Mathematics
ISBN: 0821824694

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This paper gives a classification of the tame [italic]R-orders of finite representation type in terms of their Auslander-Reiten quivers. Up to reflexive Morita equivalence one can reduce to the case of a tame order of global dimension two. Using covering theory methods, the classification is done by classifying graded orders of global dimension two, and then an interpretation of [capital Greek]Lambda as a skew group ring shows that [capital Greek]Lambda is the completion of its associated graded order.


Maximal Orders

Maximal Orders
Author: Irving Reiner
Publisher:
Total Pages: 416
Release: 1975
Genre: Language Arts & Disciplines
ISBN:

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Frobenius Groups and Classical Maximal Orders

Frobenius Groups and Classical Maximal Orders
Author: Ron Brown
Publisher: American Mathematical Soc.
Total Pages: 125
Release: 2001
Genre: Mathematics
ISBN: 0821826670

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Introduction Lemmas on truncated group rings Groups of real quaternions Proof of the classification theorem Frobenius complements with core index 1 Frobenius complements with core index 4 Frobenius complements with core index 12 Frobenius complements with core index 24 Frobenius complements with core index 60 Frobenius complements with core index 120 Counting Frobenius complements Maximal orders Isomorphism classes of Frobenius groups with Abelian Frobenius kernel Concrete constructions of Frobenius groups Counting Frobenius groups with Abelian Frobenius kernel Isomorphism invariants for Frobenius complements Schur indices and finite subgroups of division rings Bibliography


Algebraic Number Theory

Algebraic Number Theory
Author: H. Koch
Publisher: Springer Science & Business Media
Total Pages: 280
Release: 1997-09-12
Genre: Mathematics
ISBN: 9783540630036

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From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993


Basic Number Theory

Basic Number Theory
Author: Andre Weil
Publisher: Springer Science & Business Media
Total Pages: 313
Release: 2012-12-06
Genre: Mathematics
ISBN: 3662000466

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Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order

Yakov Berkovich; Zvonimir Janko: Groups of Prime Power Order
Author: Yakov G. Berkovich
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 406
Release: 2018-06-25
Genre: Mathematics
ISBN: 3110533146

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This is the sixth volume of a comprehensive and elementary treatment of finite group theory. This volume contains many hundreds of original exercises (including solutions for the more difficult ones) and an extended list of about 1000 open problems. The current book is based on Volumes 1–5 and it is suitable for researchers and graduate students working in group theory.


Algebra - Representation Theory

Algebra - Representation Theory
Author: Klaus W. Roggenkamp
Publisher: Springer Science & Business Media
Total Pages: 488
Release: 2001-08-31
Genre: Mathematics
ISBN: 9780792371137

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Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.


Stable Modules and the D(2)-Problem

Stable Modules and the D(2)-Problem
Author: F. E. A. Johnson
Publisher: Cambridge University Press
Total Pages: 282
Release: 2003-09-11
Genre: Mathematics
ISBN: 9780521537490

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This 2003 book deals with two fundamental problems in low-dimensional topology with an eye on wider context.


The Basis Problem for Modular Forms on $\Gamma _0(N)$

The Basis Problem for Modular Forms on $\Gamma _0(N)$
Author: Hiroaki Hijikata
Publisher: American Mathematical Soc.
Total Pages: 170
Release: 1989
Genre: Forms, Modular
ISBN: 0821824813

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The "basis problem'' for modular forms (of degree one) is to find a basis for a space of modular forms with elements whose Fourier coefficients can be computed explicitly. The authors give a general treatment for all cases. The main idea in the solution is to consider two kinds of forms: theta series associated with special order, and bases of primitive neben space.