Department of Mathematical Sciences
Florida Atlantic University
Boca Raton, Florida 33431-0991

Algebra-Cryptology Seminar

Spring 2003

All 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, II

Abstract.  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 Clans

Abstract.  Dr. Arnold will guide a discussion on Dedekind-like rings and representations of clans.


Tuesday, April 22, 2003, at 11:00 in 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 215
David 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 Theory

Christof Geiss and Markus Schmidmeier











Abstract.  Let  be a ring and a finite group acting on  R .  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 ring  RG  in terms of the representations of the algebra  R  and the action of  G .  In case the inclusion  of the ring of fixed points  R^G  in  R  is Galois, we obtain a Morita equivalence between R^G  and  RG .  We are going to exploit this observation in order to understand the indecomposables over the ring R[[x,y]]/(x^2+y^2) as well as over the hereditary algebras of type  B_n  and  C_n .



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

Markus Schmidmeier



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

Markus Schmidmeier



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

Representations of Clans II

David 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 Clans

David 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 215

Nonabelian Clan Categories

Fred Richman


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

A Construction for Subgroups
with a Prescribed Endomorphism Ring --- Part II

Markus 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 Subgroups
with a Prescribed Endomorphism Ring

Markus Schmidmeier

Abstract.  A category  C  is said to be  k -endowild provided each finite dimensional  k -algebra can be realized as the endomorphism ring of an object in C ; in last weeks lecture by David Arnold we have seen examples of such categories.  A nonexample is the category  of all possible embeddings  M = ( U -> V )  where U  is a subgroup of a finite abelian group V .

At least, the category  S  is controlled k -wild as we are going to show.  In fact, there is an object  in  S , the control object, which has the property that for each finite dimensional  k -algebra B  we can find an  M  in  S  such that  B  is the factor of the endomorphism ring of M  modulo the ideal  End(M)_of all maps which factor through  I .

For this, recall that the category  C  of all pairs X = ( D -> E ) where  E  is a module over the polynomial ring  k[T]  in one variable and D  is a sub vector space of  E, is k -endowild.  We are going to discuss a construction K: C -> S  which assigns to each object  X  in  C  a subgroup  M = K(X)  in  S  with the property that the factor   End(M) / End(M)_I  is isomorphic to the endomorphism ring of  X .


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

The Concept of Homotopy

Roberto 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, II

David 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 Sets

Dr. 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 Theorem

James Brewer

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


Some links to Further EventsCollege Calendar, Cryptology meetings(UCL),Algebra Conferences (FDLIST), Gainesville Algebra Year 2002-3 ,
Comments and Suggestions are 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 the Previous Programs of this seminar:  Fall 1999Spring 2000, Fall 2000, Spring 2001, Fall 2001, Spring 2002, Fall 2002
Last modified:  , by Markus Schmidmeier