Expected publication date is April 28, 2005
Description
This monograph is concerned with Galois theoretical embedding
problems of so-called Brauer type with a focus on 2-groups and on
finding explicit criteria for solvability and explicit
constructions of the solutions. The advantage of considering
Brauer type embedding problems is their comparatively simple
condition for solvability in the form of an obstruction in the
Brauer group of the ground field.
The book presupposes knowledge of classical Galois theory and the
attendant algebra. Before considering questions of reducing the
embedding problems and reformulating the solvability criteria,
the author provides the necessary theory of Brauer groups, group
cohomology and quadratic forms. The book will be suitable for
students seeking an introduction to embedding problems and
inverse Galois theory. It will also be a useful reference for
researchers in the field.
Contents
Galois theory
Inverse Galois theory and embedding problems
Brauer groups
Group cohomology
Quadratic forms
Decomposing the obstruction
Quadratic forms and embedding problems
Reducing the embedding problem
Pro-finite Galois theory
Bibliography
Index
Details:
Series: Fields Institute Monographs, Volume: 21
Publication Year: 2005
ISBN: 0-8218-3726-5
Paging: 171 pp.
Binding: Hardcover
Expected publication date is May 26, 2005
"The book gives an excellent overview of 4-manifolds, with
many figures and historical notes. Graduate students, nonexperts,
and experts alike will enjoy browsing through it."
-- Robion C. Kirby, University of California Berkeley
Description
This is a panorama of the topology of simply-connected smooth
manifolds of dimension four.
Dimension four is unlike any other dimension; it is large enough
to have room for wild things to happen, but too small to have
room to undo them. For example, only manifolds of dimension four
can exhibit infinitely many distinct smooth structures. Indeed,
their topology remains the least understood today.
The first part of the book puts things in context with a survey
of higher dimensions and of topological 4-manifolds. The second
part investigates the main invariant of a 4-manifold--the
intersection form--and its interaction with the topology of the
manifold. The third part reviews complex surfaces as an important
source of examples. The fourth and final part of the book
presents gauge theory. This differential-geometric method has
brought to light the unwieldy nature of smooth 4-manifolds; and
although the method brings new insights, it has raised more
questions than answers.
The structure of the book is modular and organized into a main
track of approximately 200 pages, which are augmented with
copious notes at the end of each chapter, presenting many extra
details, proofs, and developments. To help the reader, the text
is peppered with over 250 illustrations and has an extensive
index.
Contents
Contents of the notes
Background scenery
Higher dimensions and the h-cobordism theorem
Topological 4-manifolds and h-cobordisms
Smooth 4-manifolds and intersection forms
Getting acquainted with intersection forms
Intersection forms and topology
Classifications and counterclassifications
A survey of complex surfaces
Running through complex geometry
The Enriques-Kodaira classification
Elliptic surfaces
Gauge theory on 4-manifolds
Prelude, and the Donaldson invariants
The Seiberg-Witten invariants
The minimum genus of embedded surfaces
Wildness unleashed: The Fintushel-Stern surgery
Epilogue
List of figures and tables
Bibliography
Index
Details:
Publication Year: 2005
ISBN: 0-8218-3749-4
Paging: approximately 600 pp.
Binding: Hardcover
Expected publication date is June 2, 2005
Description
Resulting from the Tenth International Conference on
Representations of Algebras and Related Topics held at The Fields
Institute (Toronto, ON, Canada), this collection of research and
survey articles, honoring Vlastimil Dlab's seventieth birthday,
reflects state-of-the-art research on the topic.
Leading experts contributed papers, demonstrating the interaction
between representation theory of finite dimensional algebras and
neighboring subjects. A wide range of topics are covered,
including quantum groups, the theory of Lie algebras, the
geometry and combinatorics of tilting theory, commutative
algebra, algebraic geometry, homology theories, and derived and
triangulated categories. The book is suitable for graduate
students and researchers interested in the theory of algebras.
Contents
E. R. Alvares and F. U. Coelho -- On translation quivers with
weak sections
H. Asashiba -- Realization of general and special linear algebras
via Hall algebras
R. Bautista and L. Salmeron -- On discrete and inductive algebras
R. Bautista and R. Zuazua -- Exact structures for lift categories
G. Benkart and D. Moon -- Tensor product representations of
Temperley-Lieb algebras and Chebyshev polynomials
D. Benson, H. Krause, and S. Schwede -- Introduction to
realizability of modules over Tate cohomology
J. Bilodeau -- Auslander algebras and simple plane curve
singularities
I. Burban and Y. Drozd -- On derived categories of certain
associative algebras
C. Geis and I. Reiten -- Gentle algebras are Gorenstein
J. Y. Guo -- On the primeness of an Artin-Schelter regular Koszul
algebra
D. Happel and L. Unger -- On the set of tilting objects in
hereditary categories
L. Hille -- Irreudicible components, nilpotent classes, and the
Auslander algebra of k[T]/T^n
M. Hoshino and K. Nishida -- A generalization of the Auslander
formula
A. Hubery -- Representations of a quiver with automorphism:
Generalising a theorem of Kac
K. Igusa and G. Todorov -- On the finitistic global dimension
conjecture for Artin algebras
O. Khomenko -- Some applications of Gelfand-Zetlin modules
D. Kussin -- A tubular algebra with three types of separating
tubular families
V. Levandovskyy -- PBW bases, non-degeneracy conditions and
applications
D. Madsen -- Projective dimensions and Nakayama algebras
F. Marko -- Borel subalgebras of extension algebras
F. Marko -- Extesion algebras of standard modules
R. Martinez Villa and A. Martsinkovsky -- Cohomology of tails and
stable cohomology over Koszul quiver algebras
A. Neeman -- A survey of well generated triangulated categories
M. Sato -- Oneway hereditary rings
M. Schaps -- Deformations, tiltings, and decomposition matrices
R. Schiffler -- On the multiplication in the quantized enveloping
algebra of type A
A. Zavadskij -- Equipped posets of finite growth
Details:
Series: Fields Institute Communications,Volume: 45
Publication Year: 2005
ISBN: 0-8218-3415-0
Paging: 396 pp.
Binding: Hardcover
Expected publication date is May 13, 2005
Description
This volume, devoted to the 70th birthday of A. L. Onishchik,
contains a collection of articles by participants in the Moscow
Seminar on Lie Groups and Invariant Theory headed by E. B.
Vinberg and A. L. Onishchik. The book is suitable for graduate
students and researchers interested in Lie groups and related
topics.
Contents
D. N. Akhiezer -- Real forms of complex reductive groups acting
on quasiaffine varieties
A. Alexeevski -- Component groups of the centralizers of
unipotent elements in semisimple algebraic groups
D. V. Alekseevsky and V. Cortes -- Classification of pseudo-Riemannian
symmetric spaces of quaternionic Kahler type
I. V. Arzhantsev and D. A. Timashev -- On the canonical
embeddings of certain homogeneous spaces
A. G. Elashvili and V. G. Kac -- Classification of good gradings
of simple Lie algebras
S. Gindikin -- The separation of the continuous spectrum on
symmetric spaces of Cayley type
V. Gorbatsevich -- Connected sums of compact manifolds and
homogeneity
P. I. Katsylo -- On curvatures of sections of tensor bundles
Y. Khakimdjanov -- Affine structures on filiform Lie algebras
A. Lebedev, D. Leites, and I. Shereshevskii -- Lie superalgebra
structures in C^{mathbin{hbox{raise.4exhbox{bf.}}}}(mathfrak{n};mathfrak{n})
and H^{mathbin{hbox{raise.4exhbox{bf.}}}}(mathfrak{n};mathfrak{n})
A. L. Onishchik and A. A. Serov -- On isotropic super-Grassmannians
of maximal type associated with an odd bilinear form
D. I. Panyushev -- Ideals of Heisenberg type and minimax elements
of affine Weyl groups
V. L. Popov -- Projective duality and principal nilpotent
elements of symmetric pairs
V. Serganova -- On representations of Cartan type Lie
superalgebras
E. B. Vinberg -- Construction of the exceptional simple Lie
algebras
E. B. Vinberg -- Short SO_3-structures on simple Lie algebras and
associated quasielliptic planes
Details:
Series: American Mathematical Society Translations--Series 2,
Volume: 213
Publication Year: 2005
ISBN: 0-8218-3733-8
Paging: approximately 280 pp.
Binding: Hardcover