Dualities On Generalized Koszul Algebras
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| Author | : Edward L. Green |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 90 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829343 |
Koszul rings are graded rings which have played an important role in algebraic topology, noncommutative algebraic geometry and in the theory of quantum groups. One aspect of the theory is to compare the module theory for a Koszul ring and its Koszul dual. There are dualities between subcategories of graded modules; the Koszul modules.
| Author | : Robert Denk |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 130 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821833782 |
The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-sectorial operators and operator-valued Fourier multipliers. As application, we consider the $L_q$-realization of an elliptic boundary value problem of order $2m$ with operator-valued coefficients subject to general boundary conditions. We show that there is maximal $L_p$-$L_q$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.
| Author | : Yasuyuki Kachi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 133 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821832255 |
Introduction The universal pseudo-quotient for a family of subvarieties Normal bundles of quadrics in $X$ Morphisms from quadrics to Grassmannians Pointwise uniform vector bundles on non-singular quadrics Theory of extensions of families over Hilbert schemes Existence of algebraic quotient--proof of Theorem 0.3 Appendix. Deformations of vector bundles on infinitesimally rigid projective varieties with null global $i$-forms References
| Author | : Helge Glöckner |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 150 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821832565 |
A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.
| Author | : Olivier Druet |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 113 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829890 |
Function theory and Sobolev inequalities have been the target of investigation for many years. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The $AB$ programme is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. This text summarizes the results of contemporary research and gives an up-to-date report on the field.
| Author | : Donald M. Davis |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 65 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829874 |
A formula for the odd-primary v1-periodic homotopy groups of a finite H-space in terms of its K-theory and Adams operations has been obtained by Bousfield. This work applys this theorem to give explicit determinations of the v1-periodic homotopy groups of (E8,5) and (E8,3), thus completing the determination of all odd-primary v1-periodic homotopy groups of all compact simple Lie groups, a project suggested by Mimura in 1989.
| Author | : Douglas Bowman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 73 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 082182774X |
The author explores ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also found. This provides a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. Some infrastructure is also laid for more general investigations in the future
| Author | : Alan Forrest |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 137 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829653 |
This memoir develops, discusses and compares a range of commutative and non-commutative invariants defined for projection method tilings and point patterns. The projection method refers to patterns, particularly the quasiperiodic patterns, constructed by the projection of a strip of a high dimensional integer lattice to a smaller dimensional Euclidean space. In the first half of the memoir the acceptance domain is very general - any compact set which is the closure of its interior - while in the second half the authors concentrate on the so-called canonical patterns. The topological invariants used are various forms of $K$-theory and cohomology applied to a variety of both $C DEGREES*$-algebras and dynamical systems derived from such a p
| Author | : L. Rodman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 87 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829963 |
In this work, versions of an abstract scheme are developed, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results prove, amongst other things, that the band extension is continuous in an appropriate sense.
| Author | : Thierry Lévy |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 144 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821834290 |
In this memoir we present a new construction and new properties of the Yang-Mills measure in two dimensions. This measure was first introduced for the needs of quantum field theory and can be described informally as a probability measure on the space of connections modulo gauge transformations on a principal bundle. We consider the case of a bundle over a compact orientable surface. Our construction is based on the discrete Yang-Mills theory of which we give a full acount. We are able to take its continuum limit and to define a pathwise multiplicative process of random holonomy indexed by the class of piecewise embedded loops. We study in detail the links between this process and a white noise and prove a result of asymptotic independence in the case of a semi-simple structure group. We also investigate global Markovian properties of the measure related to the surgery of surfaces.
