Author: Adam NymanPublisher:
ISBN:
Category : Geometry, Algebraic
Languages : en
Pages : 180
Book Description
The Geometry of Points on Quantum Projectivizations
Author: Adam NymanPublisher:
ISBN:
Category : Geometry, Algebraic
Languages : en
Pages : 180
Book Description
Points on Quantum Projectivizations
Author: Publisher: American Mathematical Soc.
ISBN: 0821834959
Category :
Languages : en
Pages : 154
Book Description
Points on Quantum Projectivizations
Author: Adam NymanPublisher: American Mathematical Soc.
ISBN: 9780821865170
Category : Mathematics
Languages : en
Pages : 162
Book Description
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizataions, a significant class of examples in non-commutative algebraic geometry. More precisely, if $S$ is an affine, noetherian scheme, $X$ is a separated, noetherian $S$-scheme, $\mathcal{E}$ is a coherent ${\mathcal{O}}_{X}$-bimodule and $\mathcal{I} \subset T(\mathcal{E})$ is a graded ideal then we develop a compatibility theory on adjoint squares in order to construct the functor $\Gamma_{n}$ of flat families of truncated $T(\mathcal{E})/\mathcal{I}$-point modules of length $n+1$. For $n \geq 1$ we represent $\Gamma_{n}$ as a closed subscheme of ${\mathbb{P}}_{X^{2}}({\mathcal{E}}^{\otimes n})$. The representing scheme is defined in terms of both ${\mathcal{I}}_{n}$ and the bimodule Segre embedding, which we construct. Truncating a truncated family of point modules of length $i+1$ by taking its first $i$ components defines a morphism $\Gamma_{i} \rightarrow \Gamma_{i-1}$ which makes the set $\{\Gamma_{n}\}$ an inverse system. In order for the point modules of $T(\mathcal{E})/\mathcal{I}$ to be parameterizable by a scheme, this system must be eventually constant. In [20], we give sufficient conditions for this system to be constant and show that these conditions are satisfied when ${\mathsf{Proj}} T(\mathcal{E})/\mathcal{I}$ is a quantum ruled surface. In this case, we show the point modules over $T(\mathcal{E})/\mathcal{I}$ are parameterized by the closed points of ${\mathbb{P}}_{X^{2}}(\mathcal{E})$.
Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems
Author: Denis V. OsinPublisher: American Mathematical Soc.
ISBN: 0821838210
Category : Mathematics
Languages : en
Pages : 114
Book Description
In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.
Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance
Author: Marc Aristide RieffelPublisher: American Mathematical Soc.
ISBN: 0821835181
Category : Mathematics
Languages : en
Pages : 106
Book Description
By a quantum metric space we mean a $C DEGREES*$-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff di
The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups
Author: Martin W. LiebeckPublisher: American Mathematical Soc.
ISBN: 0821834827
Category : Mathematics
Languages : en
Pages : 242
Book Description
Intends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.
Maximum Principles on Riemannian Manifolds and Applications
Author: Stefano PigolaPublisher: American Mathematical Soc.
ISBN: 0821836390
Category : Mathematics
Languages : en
Pages : 118
Book Description
Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.
Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation
Author: Benoît MselatiPublisher: American Mathematical Soc.
ISBN: 0821835092
Category : Mathematics
Languages : en
Pages : 146
Book Description
Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major open question of [Dy02].
Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity
Author: Mike FieldPublisher: American Mathematical Soc.
ISBN: 0821835998
Category : Mathematics
Languages : en
Pages : 113
Book Description
On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free).
The Second Duals of Beurling Algebras
Author: Harold G. DalesPublisher: American Mathematical Soc.
ISBN: 0821837745
Category : Mathematics
Languages : en
Pages : 206
Book Description
Let $A$ be a Banach algebra, with second dual space $A""$. We propose to study the space $A""$ as a Banach algebra. There are two Banach algebra products on $A""$, denoted by $\,\Box\,$ and $\,\Diamond\,$. The Banach algebra $A$ is Arens regular if the two products $\Box$ and $\Diamond$ coincide on $A""$.