Department of Mathematical Sciences

Florida Atlantic University

Boca Raton, Florida 33431-0991

Algebra-Cryptology SeminarSpring 2003All lectures take place in Science and Engineering, room 215. Everybody is invited to participate.

Tuesday, April 29, 2003, at 2:15 in 2 15

David Arnold (Baylor and FAU)

Discussion on Dedekind-like Rings and Representations of Clans, IIAbstract. Dr. Arnold will guide a discussion on Dedekind-like rings and representations of clans.

Thursday, April 24, 2003, at 3:00 in 2 15

David Arnold (Baylor and FAU)

Discussion on Dedekind-like Rings and Representations of ClansAbstract. Dr. Arnold will guide a discussion on Dedekind-like rings and representations of clans.

Tuesday, April 22, 2003,

at 11:00in 2 15, in the Mathematical Colloquium

Dr. Thomas Bruestle (Bielefeld University)

Actions of triangular matrices.

Abstract.The invertible triangular matrices act via conjugation on the set of all triangular matrices. We study this action from different viewpoints. This leads to interesting connections between linear algebra, subgroups of abelian groups, flags of modules over the polynomial ring and representations of certain quivers.

Thursday, April 17, 2003, at 3:00 in 215David Arnold (Baylor and FAU)Dedekind-like Rings and Representations of Clans

Tuesday, April 15, 2003, at 2:15 in 2 15

David Arnold (Baylor and FAU)Butler Groups and Representations of Posets

Tuesday, April 8, 2003, at 2:15 in 2 15

Non-Commutative Galois TheoryChristof Geiss and Markus Schmidmeier

Abstract.LetRbe a ring andGa finite group acting onR. In their manuscript ``Skew Group Algebras in the Representation Theory of Artin Algebras'', Idun Reiten and Christine Riedtmann describe the category of modules over the the skew group ringRGin terms of the representations of the algebraRand the action ofG. In case the inclusion of the ring of fixed pointsR^GinRis Galois, we obtain a Morita equivalence betweenR^GandRG. We are going to exploit this observation in order to understand the indecomposables over the ringR[[x,y]]/(x^2+y^2) as well as over the hereditary algebras of typeB_nandC_n.

Tuesday, April 1, 2003, at 2:15 in 2 15Representations of Clans, IVMarkus Schmidmeier

Thursday, March 27, 2003, at 1:00 in 215Representations of Clans, IIIMarkus Schmidmeier

Tuesday, March 25, 2003, at 2:15 in 2 15

Representations of Clans IIDavid Arnold

Abstract.Clans are a powerful tool for classifying objects in representation theory, and in this talk we will apply this technology to subspace representations of a partially ordered set.

Tuesday, March 18, 2003, at 2:15 in 2 15

Representations of ClansDavid Arnold (Baylor University and FAU)

Abstract.We hope to stimulate our discussions about clans by presenting further results and examples.

Tuesday, March 11, 2003, at 2:15 in 215Tuesday, February 25, 2003, at 2:15 in 215

Nonabelian Clan CategoriesFred Richman

A Construction for Subgroupswith a Prescribed Endomorphism Ring --- Part IIMarkus Schmidmeier

Abstract.This is a continuation of the speakers previous talk to the Algebra-Cryptology Seminar.

Tuesday, February 11, 2003, at 2:15 in 2 15

A Construction for Subgroupswith a Prescribed Endomorphism RingMarkus Schmidmeier

Abstract.A categoryis said to beCk-endowild provided each finite dimensionalk-algebra can be realized as the endomorphism ring of an object in; in last weeks lecture by David Arnold we have seen examples of such categories. A nonexample is the categoryCof all possible embeddingsSM= (U->V) whereUis a subgroup of a finite abelian groupV.At least, the category

is controlledSk-wild as we are going to show. In fact, there is an objectIin, the control object, which has the property that for each finite dimensionalSk-algebraBwe can find anMinsuch thatSBis the factor of the endomorphism ring ofMmodulo the ideal End(M)_Iof all maps which factor throughI.For this, recall that the category

Cof all pairsX= (D->E) whereEis a module over the polynomial ringk[T] in one variable andDis a sub vector space ofE, isk-endowild. We are going to discuss a constructionK:->Cwhich assigns to each objectSXinCa subgroupM=K(X) inwith the property that the factor End(SM) / End(M)_Iis isomorphic to the endomorphism ring ofX.

Tuesday, February 4, 2003, at 2:15 p.m. in S&E 215

The Concept of HomotopyRoberto Ruiz

(Universidad del Valle, Cali, Colombia)

Abstract.The basics for the abstraction of homotopy from topology to "Model" categories will be given following Dan Quillen's work on the subject.

Tuesday, January 28, 2003, 2:15 p.m. in S&E 215

Representations of Finite Partially Ordered Sets, IIDavid Arnold (Baylor)

Abstract.This is a continuation of Dr. Arnolds lecture on January 21.

Tuesday, January 21, 2003, 2:15 p.m. in S&E 215

Representations of Finite Partially Ordered SetsDr. David Arnold (Baylor University, Texas)

Abstract.Properties of representations of finite partially ordered sets over fields were developed in the 1960's, in part as tools for classification of finitely generated modules over finite dimensional algebras. In particular,

there are explicit characterizations of representation type, a measure of whether or not classification is feasible. However, very little is known about representations over more general rings.In this talk I will begin with some classical problems of finding canonical forms for matrices in a representation setting and then briefly present fundamental characterizations of representation type for representations over fields. The remainder of the talk will be devoted to a summary of some recent joint work with Daniel Simson on extending these characterizations to representations of finite partially ordered sets over artinian factor rings of discrete valuation rings. These results have, via representation equivalences, immediate application to finite valuated p-groups, torsion-free abelian groups of finite rank, and lattices over orders.

Tuesday, January 14, 2003, 2:15 p.m. in S&E 215

Hilbert's Basis Theorem Implies Krull's Intersection TheoremJames Brewer

Abstract.We will give an elementary proof, due to Perdry, of the above statement.

Some links toFurther Events: College Calendar, Cryptology meetings(UCL),Algebra Conferences (FDLIST), Gainesville Algebra Year 2002-3 ,Comments and Suggestionsare welcome ! Please contact Spyros Magliveras (spyros@fau.edu), Fred Richman (richman@fau.edu), Lee Klingler(klingler@fau.edu), or Markus Schmidmeier (mschmidm@fau.edu).

For nostalgic reasons you can consult thePrevious Programsof this seminar: Fall 1999, Spring 2000, Fall 2000, Spring 2001, Fall 2001, Spring 2002, Fall 2002Last modified: , by Markus Schmidmeier