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Algebras, Rings And Their Representations: Proceedings Of The International Conference on Algebras, Modules and Rings, Lisbon, Portugal, 14-18 July 2003 PDF

403 Pages·2006·15.01 MB·English
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7flfi 9 ®fr J »•"-: ALGEBRAS, RINGS AND THEIR REPRESENTATIONS Proceedings of the International Conference on Algebras, Modules and Rings Alberto Facchini • Kent Fuller Claus M Ringel • Catarina Santa-Clara editors ALGEBRAS, RINGS AND THEIR REPRESENTATIONS Proceedings of the International Conference on Algebras, Modules and Rings ALGEBRAS, RINGS AND THEIR REPRESENTATIONS Proceedings of the International Conference on Algebras, Modules and Rings Lisbon, Portugal 14-18 July 2003 editors Alberto Facchini (Universita di Padova, Italy) Kent Fuller (University of Iowa, USA) ClauS M Ringel (Universitat Bielefeld, Germany) Catarina Santa-Clara (Universidade de Lisboa, Portugal) Cover image by courtesy of Joao Sotomayor ^p World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONGKONG • TAIPEI • CHENNAI Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ALGEBRAS, RINGS AND THEIR REPRESENTATIONS Proceedings of the International Conference on Algebras, Modules and Rings Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-256-598-1 Printed in Singapore by B & JO Enterprise CONTENTS Introduction vii Antonio Almeida Costa xv Conference Participants xix Contributors xxvii Some Coreflective Categories of Topological Modules Alina Alb 1 Inheritance of Primeness by Ideals in Lie Triple Systems A. J. Calderon Martin and M. Forero Piulestdn 7 A Geometric Approach to Four-Dimensional Absolute Valued Triple Systems Antonio J. Calderon Martin and Cdndido Martin Gonzalez 17 Divisible Modules with Respect to a Torsion Theory Iuliu Crivei and Septimiu Crivei 25 The Globalization Problem for Inner Automorphisms and Skolem- Noether Theorems Jeremy Haefner and Angel del Rio 37 Krull Monoids and Their Application in Module Theory Alberto Facchini 53 Infinite Progenerator Sums Alberto Facchini and Lawrence S. Levy 73 The Moduli Space and Versal Deformations of Three Dimensional Lie Algebras Alice Fialowski 79 Quadratic Algebras of Skew Type Eric Jespers and Jan Okniriski 93 Representation Type of Commutative Noetherian Rings (Introduction) Lee Klingler and Lawrence S. Levy 113 v VI Corner Ring Theory: A Generalization of Peirce Decompositions, I T. Y. Lam 153 Units, Principal Primes, and Generalizations of Factoriality Peter Malcolmson and Frank Okoh 183 Algebra Associated with the Principal Block of Category O for sl (C) 3 Frantisek Marko 201 Noncommutative Projective Schemes and Point Schemes Izuru Mori 215 Quasideterminants and Right Roots of Polynomials Over Division Rings Barbara L. Osofsky 241 Certains Resultats sur une Extension Minimale Mohamed Oukessou 265 •-Identities in Matrix Superalgebras with Superinvolution * Tsetska Grigorova Rashkova 273 Structure and Representations of Conformal Algebras Alexander Retakh 289 Actions of Tori and Finite Fans Sonia L. Rueda 313 Homologically Induced s[(l, 2)-Modules Jose Carlos de Sousa Oliveira Santos 329 Injective Dimension Relative to a Torsion Theory Patrick F. Smith 343 Structure Theorems on Countably Compact Rings M. Ursul 357 INTRODUCTION In memory of Professor Antonio Almeida Costa, on the centenary of his birth. Organized by Centro de Algebra da Universidade de Lisboa Held at Faculdade de Ciencias da Universidade de Lisboa http://caul.cii.fc.ul.pt/lisboa2003/ In homage to Professor Antonio Almeida Costa (1903-1978), Full Pro fessor of the Faculty of Sciences of the University of Lisbon (FCUL), and on occasion of the 100th anniversary of his birth, the Centro de Algebra da Universidade de Lisboa (CAUL) organized the "International Conference on Algebras, Modules and Rings", held at FCUL, from the 14th to the 18th of July 2003. This event was widely publicized and attracted 151 participants, from 33 different nationalities, comprising many experts in the areas of Ring and Module Theory, Representation Theory of Algebras, and other closely related fields, especially Non-Commutative Algebraic Geometry. It pro vided an excellent venue for the communication of recent results and the discussion of new problems in the areas that will surely bring about future progress in research. The invited speakers consisted of 9 main speakers, each lecturing for 50 minutes, and 9 plenary speakers, speaking for 35 minutes. The main speakers, leaders in their respective areas of research, were headed by the keynote speaker, Michel Van den Bergh, who set the tone for the confer ence, establishing a connection to Non-Commutative Algebraic Geometry. The plenary speakers are younger mathematicians, with promising work vii viii on the different subjects covered. The conference also included 85 short communications (20 minutes each). The conference was co-funded by CAUL, DMFCUL, FCUL, Fundagao para a Ciencia e a Tecnologia, Project POCTI/143/2003 of FCT and FEDER, Centro de Matematica da Universidade do Porto, Centro de Estruturas Lineares e Combinatorias and Universidade Lusofona. Grants were awarded to some participants, both by Unesco-Roste and Deutscher Akademische Austausch Dienst. The organization enjoyed some support from Turismo de Lisboa, Lisbon's City Council and Bookshop Escolar Editora. Participants had discounts on flights by TAP and VARIG. Conference Organization Scientific Committee A. Facchini (Padova) J. A. Green (Oxford, Warwick) K. Puller (Iowa) C. M. Ringel (Bielefeld) M. L. Galvao (Lisboa), coordinator D. Simson (N. Copernicus) J. L. Gomez Pardo P. F. Smith (Glasgow) (Santiago de Compostela) Organizing Committee A. P. Alexandre (Nova de Lisboa) C. Lomp (Porto) P. Carvalho Lomp (Porto) M. T. Nogueira (Lisboa) A. V. Fonseca (Lusofona, Leicester) C. Santa-Clara (Lisboa), coordinator M. L. Galvao (Lisboa) M. E. Simoes (Lisboa) Assistants to the Organization Staff: M. Manuela Ferreira, Beatrice Huberty. Students: Catarina Barroca, Patricia Batista, Marta Cabrita, Eliana Cas tro, Vidal Delgado, Antonio V. Dias, M. Graga Duffner, Gilda M. Fer reira, Susana Frederique, Jaime Gaspar, Joaquim Graga, Joana M. Matos, Rita Monge, Alexandra Passinhas, Ana Pinheiro, David Raimundo, Filipe Ramos, Andrea Rodrigues, Carina Rodrigues, Ana Isabel Teixeira, Ana Margarida Troncao. ix Invited Talks Keynote M. Van den Bergh (Limburgs-Diepenbeek): Derived categories in algebraic geom etry Main Talks S. Koenig (Leicester): Comparing Schur algebras, upwards and downwards T.-Y. Lam (California, Berkeley): Corner Ring Theory: A Generalization of Peirce Decompositions L. Levy (Nebraska, Lincoln and Wisconsin, Madison): Representation type of Commutative Noetherian Rings 0. Mathieu (Claude Bernard, Lyon): Connection on stable bundle B. Osofsky (Rutgers, New Brunswick): Quasideterminants and Roots of Polyno mials over Division Rings C. M. Ringel (Bielefeld): Basic properties of the module category of an artin algebra M. Saorin (Murcia): Categorical invariance of automorphism groups of rings an al gebras J. Trlifaj (Karlova, Praha): Cotorsion pairs Plenary Talks P. Ara (Autonoma, Barcelona): Finitely presented modules over Leavitt algebras J. A. de la Pena (UNAM, Mexico City): Hochschild cohomology of algebras and epimorphisms 1. Gordon (Glasgow): Rational Cherednik algebras and applications P. A. Guil Asensio (Murcia): Left Cotorsion Rings O. Iyama (Himeji): Representation dimension of artin algebras J. Okniriski (Warsaw): Quadratic algebras of skew type C. Santa-Clara (Lisboa): Goldie dimension applied to Linear Operator Theory J. Schroer (Leeds): A decomposition theory for irreducible components of module varieties A. Tonolo (Padova): Cotilting modules versus canonical modules for Cohen-Macaulay rings Contributed talks Module Theory Klaus Robert Aehle: Complexity of degenerations of modules Khaled Al-Takhman: Comatrix Corings Lidia Angeleri Hugel: Tilting modules and Gorenstein rings Maria Jose Arroyo Paniagua: Spectral Torsion Theories and a General Theory of Types Septimiu Crivei: On divisible modules with respect to a torsion theory Sergio Estrada: Torsion free covers of cotorsion modules Alberto Facchini: Projective modules and divisor homomorphisms Grigory Garkusha: Triangulated categories and the Ziegler spectrum Enrico Gregorio: Cotilting dualities

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Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and non-commutative rings, modules, conformal algebras, and torsion theories. The volume collects stimulating discussions from world-renowned name
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