Division Algebras and Invariant Fields
除法代数和不变域
基本信息
- 批准号:9970213
- 负责人:
- 金额:$ 34.83万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:1999
- 资助国家:美国
- 起止时间:1999-06-01 至 2005-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
SALTMAN 9970213Professor Saltman proposes to study questions concerning division algebras and invariant fields. In the area of division algebras, he will study questions that all involve ways of describing these objects. One series of questions concern special, so called semidirect product, division algebras with arbitrary ground field. He is asking whether they are even more special cyclic algebras. Another series of questions in involve considering general division algebras with special ground fields, in this case function fields of curves over p-adics, and asking whether they are cyclic. The second area of study of Professor Saltman, invariant fields, will also have two strands. The first series of questions concern trying to use Galois cohomology to show certain of these fields are nonrational. The second series of questions involve simply studying these invariant fields and, for example, investigating division algebras with these invariant fields as center. Division algebras are simple objects that have been studied for over a hundred years. The basic idea is to consider finite dimensional vector spaces with a product that is well behaved. That is, the product is associative and, as in the real numbers, every nonzero element has an inverse, but the product is noncommutative (i.e. a times b is not b times a). It turns out the these objects embody deep properties of their centers which are the more familiar ``fields'' like the rationals or the reals. Describing all division algebras with a fixed center is really saying something deep about the arithmetic of this center. There are ``generic'' or very general division algebras whose properties in some ways reflect the properties of all division algebras. Their centers are, however, hard to understand so called invariant fields. One can directly study these invariant fields and thereby understand more about division algebras. One can use, as tools in this study, a whole array of mathematics including algebraic geometry, Galois cohomology, and algebraic K-theory.
Saltman 9970213 Saltman教授建议研究有关除法代数和不变域的问题。在该地区的司代数,他将研究的问题,所有涉及的方式来描述这些对象。一系列的问题涉及特殊的,所谓的半直积,除代数与任意基域。他在问它们是否是更特殊的循环代数。另一系列的问题涉及考虑一般司代数与特殊的地面领域,在这种情况下功能领域的曲线p-adics,并询问他们是否循环。Saltman教授的第二个研究领域,不变场,也将有两条链。第一系列的问题涉及试图使用伽罗瓦上同调,以显示某些领域是非理性的。第二系列的问题涉及简单地研究这些不变领域,例如,调查部门代数与这些不变领域为中心。除代数是一个简单的对象,已经研究了一百多年。其基本思想是考虑有限维向量空间的产品是良好的行为。也就是说,乘积是结合的,并且和真实的数一样,每个非零元素都有逆元素,但是乘积是非交换的(即a乘以B不是B乘以a)。事实证明,这些对象体现了它们中心的深层属性,这些属性是更熟悉的“场”,如有理数或实数。描述所有具有固定中心的除代数实际上是在说一些关于这个中心的算术的深层次的东西。有“一般的”或非常一般的除代数,其性质在某些方面反映了所有除代数的性质。然而,它们的中心很难理解所谓的不变场。人们可以直接研究这些不变域,从而对除代数有更多的了解。人们可以使用,作为工具,在这项研究中,整个阵列的数学,包括代数几何,伽罗瓦上同调,代数K理论。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
David Saltman其他文献
Évaluation d’une clinique de suivi téléphonique gérée par des infirmières pour les patients porteurs de cancers hématologiques indolents et chroniques : une étude pilote
对癌症、血液病和慢性病患者的体弱者电话诊所的评估:飞行员练习曲
- DOI:
- 发表时间:
2008 - 期刊:
- 影响因子:0
- 作者:
Aldyn Overend;Kong Khoo;M. Delorme;V. Krause;Ardashes Avanessian;David Saltman - 通讯作者:
David Saltman
Bimodule structure of central simple algebras
- DOI:
10.1016/j.jalgebra.2016.07.039 - 发表时间:
2017-02-01 - 期刊:
- 影响因子:
- 作者:
Eliyahu Matzri;Louis H. Rowen;David Saltman;Uzi Vishne - 通讯作者:
Uzi Vishne
David Saltman的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('David Saltman', 18)}}的其他基金
Division Algebras and Field Invariants
除法代数和场不变量
- 批准号:
0401468 - 财政年份:2004
- 资助金额:
$ 34.83万 - 项目类别:
Continuing Grant
Mathematical Sciences: Brauer Groups and the Theory of Fields
数学科学:布劳尔群和场论
- 批准号:
9400650 - 财政年份:1994
- 资助金额:
$ 34.83万 - 项目类别:
Continuing Grant
Mathematical Sciences: Division Algebras, Brauer Groups, andField Theory
数学科学:除代数、布劳尔群和场论
- 批准号:
8901778 - 财政年份:1989
- 资助金额:
$ 34.83万 - 项目类别:
Continuing Grant
Mathematical Sciences: Division Algebras, Brauer Groups, andField Theory
数学科学:除代数、布劳尔群和场论
- 批准号:
8601279 - 财政年份:1986
- 资助金额:
$ 34.83万 - 项目类别:
Continuing Grant
Mathematical Sciences: Division Algebras, Brauer Groups and Field Theory
数学科学:除代数、布劳尔群和场论
- 批准号:
8303356 - 财政年份:1983
- 资助金额:
$ 34.83万 - 项目类别:
Continuing Grant
Mathematical Sciences Postdoctoral Research Fellowship
数学科学博士后研究奖学金
- 批准号:
8017160 - 财政年份:1980
- 资助金额:
$ 34.83万 - 项目类别:
Fellowship Award
相似海外基金
On the range of invariant problem for inductive limit type actions of Z_2 on AF algebras
AF代数上Z_2归纳极限型作用不变问题的范围
- 批准号:
573357-2022 - 财政年份:2022
- 资助金额:
$ 34.83万 - 项目类别:
University Undergraduate Student Research Awards
INVARIANT ALGEBRAS IN HYPERBOLIC GEOMETRY
双曲几何中的不变代数
- 批准号:
EP/V048546/1 - 财政年份:2021
- 资助金额:
$ 34.83万 - 项目类别:
Research Grant
Study of the splitting-*-homomorphisms by ordered zero completely positive maps and the heredity of invariant properties of C*-algebras
有序零完全正映射的分裂-*-同态及C*-代数不变性质的遗传性研究
- 批准号:
20K03644 - 财政年份:2020
- 资助金额:
$ 34.83万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Invariant convexity in infinite dimensional Lie algebras
无限维李代数中的不变凸性
- 批准号:
320351428 - 财政年份:2016
- 资助金额:
$ 34.83万 - 项目类别:
Research Grants
Quantised algebras, supersymmetry and invariant theory
量子化代数、超对称性和不变理论
- 批准号:
DP120103432 - 财政年份:2012
- 资助金额:
$ 34.83万 - 项目类别:
Discovery Projects
Invariant Theory for Finite-Dimensional Algebras
有限维代数不变理论
- 批准号:
1101383 - 财政年份:2011
- 资助金额:
$ 34.83万 - 项目类别:
Standard Grant
Research on variants of the polynomial invariant of Hopf algebras
Hopf代数多项式不变量的变体研究
- 批准号:
22540058 - 财政年份:2010
- 资助金额:
$ 34.83万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Invariant Subspaces and Free Probability in the Context of von Neumann algebras
冯诺依曼代数背景下的不变子空间和自由概率
- 批准号:
0300336 - 财政年份:2003
- 资助金额:
$ 34.83万 - 项目类别:
Continuing Grant
Representation Theory and Invariant Means on C*-algebras
C*-代数的表示论和不变均值
- 批准号:
0244807 - 财政年份:2003
- 资助金额:
$ 34.83万 - 项目类别:
Standard Grant
Invariant Theory of Finite Groups and Finite-Dimensional Hopf Algebras
有限群不变论和有限维Hopf代数
- 批准号:
9988756 - 财政年份:2000
- 资助金额:
$ 34.83万 - 项目类别:
Continuing Grant