Time and
place. The algebra seminar this term will be on Wednesdays,
- when at UO: from 3:20 to 4:20 in room KED B-015
- when at Carleton: from 3:00 to 4:00 in room HP 4351
(McPhail).
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
Abstract:
A Q-homology plane is a complex normal surface whose rational
cohomology is the same as that of the affine plane C
^{2}. Since
Ramanujam's discovery of a contractible affine surface non-isomorphic
to C
^{2} 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 C
^{3} are linearizable.
Speaker: Ben Steinberg (Carleton)
Title: Quivers of monoids with basic algebras
Time: Wednesday
February 16,
3-4pm
Place: Room HP4351, Carleton University
Abstract:
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.
Speaker:
Title:
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
Abstract:
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
Abstract:
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
Abstract:
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
Abstract:
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