Representations of Algebras: Proceedings of the Third International Conference on Representations of Algebras Held in Puebla, Mexico, August 4–8 1980

386 Pages·1981·4.31 MB·English

by  Raymundo Bautista

Lecture Notes ni
Mathematics
Edited by .A Dold dna .B nnamkcE
903
snoitatneserpeR
fo Algebras
Proceedings of the Third International
Conference on Representations of Algebras
Held ni Puebla, Mexico, August 4-8 1980
Edited by .M Auslander and .E Lluis
galreV-regnirpS
Berlin Heidelberg New York 1891
srotidE
Maurice Auslander
Department of Mathematics
Brandeis University
Waltham, MA 02154, USA
Emilo Lluis
Instituto de Matems.ticas - U.N.A.M.
Area de la Investigaci6n Cientifica
Circuito Exterior, Cd. Universitaria
M6xico 20, D.F. Mexico
AMS Subject Classificatio0s (1980): 16A18, 16A26, 16A46,1 6A64,
71 B10, 71 B35, 18XXX, 20 CXX.
ISBN 3-540-11179-4 Springer-Verlag Berlin Heidelberg NewYork
ISBN 0-387-11179-4 Springer-Verlag NewYork Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole or
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similar and means, storage ni data banks. Under w 54 of the German Copyright
Law where copies are fomra de other than private a use, fee is to payable
"Verwertungsgesellschaft Wort", Munich.
(cid:14)9 by Springer-Verlag Berlin Heidelberg 1891
Printed ni Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
2141/3140-543210
FOREWORD
These Proceedings contain research papers based on the lectures
given at the Third International Conference on Representations of
Algebras held August 8-16, 1980 in Puebla, Mexico. A Workshop pre-
ceded the Conference (August 4-8) and the corresponding reports will
be published separately.
Not all contributions to the Conference appear in these Pro-
ceedings; on the other hand, some papers which were not reported but
were a consequence of the meeting, are included.
It is the editors hope that the present volume will offer to
the workers in this area a realistic survey of the recent advances and
trends in this rapidly growing field.
The meeting was financially supported by
(cid:12)9 Subdirecci6n de Investigaci6n Cientffica de la Secretarfa de
Educaci6n P~blica.
(cid:12)9 Consejo Nacional de Ciencia y Tecnologfa.
(cid:12)9 Instituto de Matem~ticas de la Universidad Nacional Aut6noma
de M~xico.
(cid:12)9 Universidad Aut6noma de Puebla.
The Universidad Aut6noma de Puebla not only gave financial
support but also unforgettably warm hospitality.
We would like to thank the Organizing Committee
Jonathan Alperin (Chicago) Gerhard O. Michler (Essen)
Maurice Auslander (Brandeis) Irving Reiner (Urbana)
Raymundo Bautista (M~xico) Idun Reiten (Trondheim)
Vlastimil Dlab (Carleton) Claus Ringel (Bielefeld)
Peter Gabriel (Z~rich) Andrej V. Roiter (Kiev)
Roberto Martfnez (M~xico)
VI
the Local Organizing Committee
Raymundo Bautista Emilio Lluis
Humberto C~rdenas Roberto Martfnez
Octavio Garcfa
as well as Ms. Lourdes Arceo for her efficient secretarial services.
We also wish to thank Springer Verlag for its cooperation in
publishing these Proceedings in Lecture Notes.
LIST OF LECTURES
J.L. ALPERIN The Green correspondence and
Brauer's induction theorem
M. AUSLANDER - S.O. SMAL@* Almost split sequences in
subcategories
R. BAUTISTA - S. BRENNER* On the number of terms in the
middle of an almost split sequence
and related results
R. BAUTISTA - L. COLAVITA On adjoint functors in
L. SALMERON* representation theory ist Part
R. BAUTISTA - F. LARRION* Auslander-Reiten quivers for
certain algebras of f.r.t.
K. BONGARTZ On representation-finite tree
algebras
D.W. BURRY Recent work in vertex theory
M.C.R. BUTLER Grothendieck groups and almost
split sequences
J.F. CARLSON Complexity and Krull dimension
L. CHASTKOFSKY Modular characters of finite
Chevalley groups
P. FLEURY Remarks on local modules
P. FONG On blocks of GL(n,q) with
abelian defect groups
K.R. FULLER Diserial rings and standard
modules
IV
P. GABRIEL Coverings in representation theory
E.L. GREEN Graded artin algebras and their
representations
D. HAPPEL Relative invariants and subgeneric
orbits of quivers of finite and
tame type
M. HAZEWINKEL Symmetric groups, the specializa-
tion order, systems and Grassmann
manifolds
G.D. JAMES How to obtain new representations
of a group from a given represen-
tation
M. KLEINER Induced modules and comodules and
representations of BOCS's and
DGC's
R. KNORR A special case of a conjecture of
R. Brauer
S. KOSHITANI Some remarks on the modular group
of algebras
O. KROLL** Complexity and elementary abelian
groups
P. LANDROCK Blocks with normal defect groups
and the extended first main
theorem
S. LOPEZ DE MEDRANO Topological aspects of matrix
problems
N. MARMARIDIS Some remarks on reflection
functors
VII
R. MARTINEZ-VILLA Algebras stably equivalent to
factors of hereditary
G. MICHLER On the blocks with multiplicity
one
K. MORRISON The connected component group of
an algebra
W. MULLER Generalized fibred sums of
indecomposable modules
F. OKOH Cotorsion modules over tame
hereditary finite-dimensional
algebras
J. OLSSON Inequalities for block theoretic
invariants
M.I. PLATZECK - G. TODOROV* TrD-periodic modules over
selfinjective algebras
W. PLESKEN Compatible decompositions of
lattices over orders
C.M. RINGEL Tilted algebras
A.V. ROJTER Representations of quivers with
involution
G. SCHNEIDER On the 2-modular representations
of M12
D. SIMSON A class of artinian rings of
finite representation type
B. SRINIVASAN An analogue of the Nakayama
conjecture for GL(n,q)
H. TACHIKAWA Trivial extensions of reflection
functors
~LIV
J, WASCHBUSCH Representations of self-injective
algebras
A. WIDEMANN Auslander-Reiten-Graphs of orders
and blocks of cyclic defect two
W. WILLEMS What conditions do vertices of
irreducible modules satisfy?
K. YAMAGATA On algebras whose trivial
extensions are of finite
representation type
D. ZACHARIA Preprojective partitions for
hereditary artin algebras of
F,R.T.
* denotes the speaker
** lecture delivered by J.L. Alperin
LIST OF REGISTERED PARTICIPANTS
ALFEREZ Ma. Guadalupe, Universidad Nac. Aut6noma de M~xico, Mexico.
ALPERIN Jonathan L., University of Chicago, Chicago, Illinois, U.S.A.
ASSEM Ibrahim, Carleton University, Ottawa, Ontario, Canada.
AUSLANDER Bernice, University of Massachusetts, Boston, Mass., U.S.A.
AUSLANDER Maurice, Brandeis University, Waltham, Mass., U.S.A.
BAUTISTA Raymundo, Universidad Nac. Aut6noma de M~xico, Mexico.
BERGER Thomas R., University of Minneapolis, Minneapolis, Minn. U.S.A.
BONGARTZ Klaus, Unlversltat (cid:12)9 . . Zurlch, I! . Switzerland.
BRENNER Sheila, University of Liverpool, United Kingdom.
BURRY David, Yale University, New Haven, Connecticut, U.S.A.
BUTLER M.C.R., University of Liverpool, United Kingdom.
CARDENAS Humberto, Universidad Nac. Aut6noma de M~xico, Mexico.
CARLSON J.F., University of Georgia, Athens, U.S.A.
CHASTKOFSKY Leonard, Massachusetts Institute of Technology, Cambridge,
Massachusetts, U.S.A.
CIBILS Claudio, Universidad Nac. Aut6noma de M~xico, Mexico.
CLINE Edward, Clark University, Worcester, Massachusetts, U.S.A.
COLAVITA Carmen G6mez de, Universidad Nac. Aut6noma de M~xico, Mexico.
COLAVITA Luis, Universidad Nac. Aut6noma de M~xico, Mexico.
CONTI Benedetto, Universit~ de Fribourg, Fribou~g, Switzerland.
COTA MEZA, Ruben, Universidad Aut6noma de Puebla, Puebla, Mexico.
DAVILA OJEDA, Flavio, Escuela de Ffsico-Matem~ticas, Instituto
Polit~cnico Nacional, Mexico.
DLAB Vlastimil, Carleton University, Ottawa, Ontario, Canada.
DOWBOR Piotr, University of Torun, Poland.
ECHEVERRIA CRENNA, Adriana, Universidad Aut6noma de Puebla, Puebla
Mexico.
ERDMANN Karin, Universltat (cid:12)9 I! Essen, Essen, West Germany.
FLEURY Patrik J., State University of New York, Plattsburgh, New York
U.S.A.
FONG Paul, University of Illinois at Chicago Circle, Chicago, Illinois
U.S.A.
FULLER Kent R., University of Iowa, Iowa, U.S.A.
GABRIEL Peter, Unlversltat (cid:12)9 . I! Zurzch, . . Switzerland.
GALVAN NAVARRO AndrOs, Escuela de Ffsico-Matem~ticas, Instituto
Polit~cnico Nacional, Mexico.
GARCIA O.C., Universidad Nac. Aut6noma de M~xico, Mexico.
GLAZMAN NOWLASKI Mary, Universidad Nac. Aut6noma de M~xico, Mexico.
GOMEZ-MONT, Xavier, Universidad Nae. Aut6noma de M~xico, Mexico.
GONZALEZ, Marcela, Universidad NaC. Aut6noma de M~xico, Mexico.
GREEN Edward L., Virginia Polytechnic Institute, Blacksburg, U.S.A.
GUSTAFSON William H., Texas Tech. University, Lubbock, Texas, U.S.A.
HAPPEL Dieter, Universitat I! Bielefeld, West Germany/Carleton University
Ottawa, Ontario, Canada.
HAZEWINKEL Michiel, Erasmus Univ. Rotterdam, Holland.
HUGHES David, University of Liverpool, United Kingdom.
IWANAGA Yasuo, University of Tsukuba, Ibaraki, Japan/Carleton
University, Ottawa, Ontario, Canada.
JAMES G.D., Sidney Sussex College, Cambridge, United Kingdom.
~ONES Alfredo, Universidade de Sao Paulo, Brasil.
JOHNSON K.W., University of The West Indies, Kingston, Jamaica.
JUAREZ RAMIREZ Araceli, Universidad Aut6noma de Puebla, Puebla, Mexico.
KLEINER Mark, Brandeis University, Waltham, Massachusetts, U.S.A.
KN6RR Reinhard, University of Illinois, Urbana, Ill., U.S.A.
KOSHITANI Shigeo, Chiba University, Chiba, Japan.
KRAFT Hanspeter, Mathematisches Institut, Bonn, West Germany.
LANDROCK Peter, Aarhus University, Denmark.
LARRION Francisco, Universidad Nac. Aut6noma de M~xico, Mexico.
LOPEZ DE MEDRANO Santiago, Universidad Nac. Aut6noma de M~xico, Mexico.