Algebra Seminar (winter 2011)
Department of Mathematics & Statistics
University of Ottawa
Faculté des sciences
Faculty of Science

Time and place.  The algebra seminar this term will be on Wednesdays,
SHUTTLE BUS:  leaves UO at 2:30 and arrives at Carleton at 2:50; leaves Carleton at 4:25 and arrives at UO at 4:45.

Speaker:  Karol Palka (UQAM)
Title:  On Q-homology planes
Time: Wednesday February 9, 3:20-4:20 pm
Place: KED B-015, University of Ottawa

A Q-homology plane is a complex normal surface whose rational cohomology is the same as that of the affine plane C2. Since Ramanujam's discovery of a contractible affine surface non-isomorphic to C2 fourty years ago, the world of these surfaces has been intensively analyzed. Because of their similarity to the plane they play in particular an important role as a source of examples and counterexamples. While their complete counterparts, the fake projective planes, are well understood, the Q-homology planes still require more studies. Recently we have completed the classification of singular Q-homology planes having smooth locus of non-general type. We discuss the structure theorems and some examples. If time permits, we also discuss a recent theorem (joint work with M. Koras) generalizing a result of Koras-Russell which was a crucial step in the proof that algebraic C-actions on C3 are linearizable.

Speaker: Ben Steinberg (Carleton)
Title:  Quivers of monoids with basic algebras
Time: Wednesday February 16, 3-4pm
Place: Room HP4351, Carleton University


In recent years, a number of people in algebraic combinatorics and probability, including Aguiar, Berg, Bergeron, Bhargava, Bidigare, Bjorner, Brown, Denton, Diaconis, Hanlon, Hivert, Hsiao, Mahajan, Rockmore, Saliola, Schilling and Thiery have written papers where the representation theory of certain finite monoids with basic algebras plays a central role.  The monoids in question are closely related to the representation theory of finite Coxeter groups.

In joint work with Margolis, we have computed the quiver of an arbitrary finite monoid with a basic algebra (in characteristic 0).  The computation requires knowledge of the character table of certain groups and computing certain equivalence relations on subsets of the monoid.

For a certain subclass, which contains all the examples considered by the people above, we can also compute the Cartan invariants and give "multiplicative bases" for the projective indecomposables (i.e., a basis B such that B\cup \{0\} is invariant under the action of the monoid).

We will try to sketch as much of this as we can during the talk.

Time: Wednesday March 2, 3-4pm
Place: Room HP4351, Carleton University

Speaker: Erhard Neher (UO)
Title:  Steinberg Groups and Jordan pairs
Time: Wednesday March 9, 3:20-4:20 pm
Place: KED B-015, University of Ottawa


In this talk I will describe a concrete construction of groups as groups of automorphisms of certain Lie algebras and an abstract construction by generators and relations. The concrete groups in question cover most classical groups over rings and also make their appearance in geometry. The abstract groups are called Steinberg groups because they generalize the groups defined by Steinberg (that is Robert Steinberg, not Ben). The two types of groups are related via central extensions. The main methods to make the constructions work come from Jordan pairs, but no prior knowledge of Jordan pairs will be assumed.

Speaker: Alok Maharana (McGill)
Title:  Cyclic covers of the affine plane
Time: Wednesday March 16, 3:20-4:20 pm
Place: KED B-015, University of Ottawa


Smooth affine complex algebraic surfaces with same rational homologies as the affine plane are called Q-homology planes. It is known that such a surface is rational. These surfaces play an important role in affine geometry because of their relation to the Cancellation problem, Jacobian conjecture and the study of reductive group action on affine spaces. In this talk we shall show how to classify all Q-homology planes which are cyclic covers of the affine plane. This provides many examples of hypersurface Q-homology planes.

Speaker: Amir Barghi (Carleton & Tehran)
Title:  Representation of Table Algebras
Date: Wednesday March 23, 3-4pm,
Place: room HP4351, Carleton University

A table algebra is a C-algebra with nonnegative structure constants was introduced by [Z. Arad,  E. Fisman, M. Muzychuk, On the Product of Two Elements in Noncommuatative C-Algebras, Algebra Colloquium, 5:1, 85-97, 1998]. It is well known that the complex adjacency algebra of an association scheme (or homogeneous coherent configuration) is an integral table algebra. On the other hand, the  adjacency algebra of an association scheme has a special module, namely the standard module, that  contains the regular module as a submodule. The character afforded by the standard module is called  the standard character, [D. G. Higman, Coherent Configurations, Part(I): Ordinary Representation Theory, Geometriae Dedicata, 4, 1-32, 1975]. This leads us to generalize the concept of standard character from adjacency algebras to table algebras. As an application of this generalization, we provide a necessary and sufficient condition for a table algebra to originate from an association scheme.

Speaker: Alexey Gordienko (Memorial U.)
Title:  Codimensions of polynomial identities of representations of Lie algebras
Time: Wednesday March 30, 3:20-4:20 pm
Place: KED B-015, University of Ottawa


Codimensions are the simplest numeric characteristics of polynomial identities.  In 1980's, conjectures about their asymptotic behavior were made by Amitsur and Regev.  Amitsur's conjecture was proved in 1999 by M.V. Zaicev and A. Giambruno for associative algebras and in 2002 by M.V. Zaicev for finite dimensional Lie algebras. We shall discuss the analog of Amitsur's conjecture for polynomial identities of representations of Lie algebras.

Speaker: Nikita Karpenko (Jussieu)
Title:  TBA
Time: Wednesday April 6, 3:20-4:20 pm
Place: KED B-015, University of Ottawa

Abstract:  TBA