Points on Quantum Projectivizations

Points on Quantum Projectivizations PDF Author:
Publisher: American Mathematical Soc.
ISBN: 0821834959
Category :
Languages : en
Pages : 154

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Book Description

Points on Quantum Projectivizations

Points on Quantum Projectivizations PDF Author:
Publisher: American Mathematical Soc.
ISBN: 0821834959
Category :
Languages : en
Pages : 154

Get Book Here

Book Description


Points on Quantum Projectivizations

Points on Quantum Projectivizations PDF Author: Adam Nyman
Publisher: American Mathematical Soc.
ISBN: 9780821865170
Category : Mathematics
Languages : en
Pages : 162

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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 ${\mathbb{P}}_{X^{2}}(\mathcal{E})$.

The Geometry of Points on Quantum Projectivizations

The Geometry of Points on Quantum Projectivizations PDF Author: Adam Nyman
Publisher:
ISBN:
Category : Geometry, Algebraic
Languages : en
Pages : 180

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Book Description


Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations

Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations PDF Author: Greg Hjorth
Publisher: American Mathematical Soc.
ISBN: 0821837710
Category : Mathematics
Languages : en
Pages : 126

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Book Description
Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.

Integral Transformations and Anticipative Calculus for Fractional Brownian Motions

Integral Transformations and Anticipative Calculus for Fractional Brownian Motions PDF Author: Yaozhong Hu
Publisher: American Mathematical Soc.
ISBN: 0821837044
Category : Mathematics
Languages : en
Pages : 144

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Book Description
A paper that studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error.

Uniformizing Dessins and BelyiMaps via Circle Packing

Uniformizing Dessins and BelyiMaps via Circle Packing PDF Author: Philip L. Bowers
Publisher: American Mathematical Soc.
ISBN: 0821835238
Category : Mathematics
Languages : en
Pages : 118

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Book Description
Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.

A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields

A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields PDF Author: Jason Fulman
Publisher: American Mathematical Soc.
ISBN: 0821837060
Category : Mathematics
Languages : en
Pages : 104

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Book Description
Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.

The Second Duals of Beurling Algebras

The Second Duals of Beurling Algebras PDF Author: Harold G. Dales
Publisher: American Mathematical Soc.
ISBN: 0821837745
Category : Mathematics
Languages : en
Pages : 206

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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 $A""$.

Kleinian Groups which Are Limits of Geometrically Finite Groups

Kleinian Groups which Are Limits of Geometrically Finite Groups PDF Author: Ken'ichi ƌshika
Publisher: American Mathematical Soc.
ISBN: 0821837729
Category : Mathematics
Languages : en
Pages : 136

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Book Description
Ahlfors conjectured in 1964 that the limit set of every finitely generated Kleinian group either has Lebesgue measure $0$ or is the entire $S^2$. This title intends to prove that this conjecture is true for purely loxodromic Kleinian groups which are algebraic limits of geometrically finite groups.

Entropy Bounds and Isoperimetry

Entropy Bounds and Isoperimetry PDF Author: Serguei Germanovich Bobkov
Publisher: American Mathematical Soc.
ISBN: 082183858X
Category : Computers
Languages : en
Pages : 88

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Book Description
In these memoirs Bobkov and Zegarlinski describe interesting developments in infinite dimensional analysis that moved it away from experimental science. Here they also describe Poincar -type inequalities, entropy and Orlicz spaces, LSq and Hardy-type inequalities on the line, probability measures satisfying LSq inequalities on the real line, expo