scholarly journals Essential dimension of spinor and Clifford groups

2014 ◽  
Vol 8 (2) ◽  
pp. 457-472 ◽  
Author(s):  
Vladimir Chernousov ◽  
Alexander Merkurjev
Keyword(s):  
Essential Dimension ◽  
Clifford Groups

scholarly journals Spinors and essential dimension

2017 ◽  
Vol 153 (3) ◽  
pp. 535-556 ◽  
Author(s):  
Skip Garibaldi ◽  
Robert M. Guralnick
Keyword(s):  
Number Theory ◽  
Characteristic Zero ◽  
Quadratic Forms ◽  
Low Rank ◽  
Essential Dimension ◽  
Base Field ◽  
Spin Groups ◽  
Group Schemes ◽  
Clifford Groups

We prove that spin groups act generically freely on various spinor modules, in the sense of group schemes and in a way that does not depend on the characteristic of the base field. As a consequence, we extend the surprising calculation of the essential dimension of spin groups and half-spin groups in characteristic zero by Brosnan et al. [Essential dimension, spinor groups, and quadratic forms, Ann. of Math. (2) 171 (2010), 533–544], and Chernousov and Merkurjev [Essential dimension of spinor and Clifford groups, Algebra Number Theory 8 (2014), 457–472] to fields of characteristic different from two. We also complete the determination of generic stabilizers in spin and half-spin groups of low rank.

scholarly journals 306 Sociodemographic disparities: an essential dimension of gonorrhea in pregnancy in the United States 2016-2018

2021 ◽  
Vol 224 (2) ◽  
pp. S200-S201
Author(s):  
Eran Bornstein ◽  
Yael Eliner ◽  
Moti Gulersen ◽  
Amos Grunebaum ◽  
Erez Lenchner ◽  
...  
Keyword(s):  
United States ◽  
The United States ◽  
Essential Dimension ◽  
Sociodemographic Disparities ◽  
In Pregnancy

scholarly journals Fields of Definition for Representations of Associative Algebras

2018 ◽  
Vol 62 (1) ◽  
pp. 291-304
Author(s):  
Dave Benson ◽  
Zinovy Reichstein
Keyword(s):  
Finite Extension ◽  
Representation Type ◽  
Essential Dimension ◽  
Extension Field ◽  
Associative Algebras ◽  
Separable Extension ◽  
Finite Representation ◽  
Field Of Definition ◽  
Finite Dimensional ◽  
A Finite Group

AbstractWe examine situations, where representations of a finite-dimensionalF-algebraAdefined over a separable extension fieldK/F, have a unique minimal field of definition. Here the base fieldFis assumed to be a field of dimension ≼1. In particular,Fcould be a finite field ork(t) ork((t)), wherekis algebraically closed. We show that a unique minimal field of definition exists if (a)K/Fis an algebraic extension or (b)Ais of finite representation type. Moreover, in these situations the minimal field of definition is a finite extension ofF. This is not the case ifAis of infinite representation type orFfails to be of dimension ≼1. As a consequence, we compute the essential dimension of the functor of representations of a finite group, generalizing a theorem of Karpenko, Pevtsova and the second author.

Obstetric Ethics: An Essential Dimension in Planned Home Birth

2011 ◽  
Vol 118 (2, Part 1) ◽  
pp. 357 ◽  
Author(s):  
Nicholas S. Fogelson ◽  
Stuart Fischbein
Keyword(s):  
Home Birth ◽  
Essential Dimension ◽  
Planned Home Birth

Feature-Linking Model for Image Enhancement

2016 ◽  
Vol 28 (6) ◽  
pp. 1072-1100 ◽  
Author(s):  
Kun Zhan ◽  
Jicai Teng ◽  
Jinhui Shi ◽  
Qiaoqiao Li ◽  
Mingying Wang
Keyword(s):  
Neural Networks ◽  
Image Enhancement ◽  
Human Visual System ◽  
Input Image ◽  
Temporal Coding ◽  
Essential Dimension ◽  
Neural Representations ◽  
Gamma Band Oscillations ◽  
Processing Mechanisms ◽  
Enhancement Algorithm

Inspired by gamma-band oscillations and other neurobiological discoveries, neural networks research shifts the emphasis toward temporal coding, which uses explicit times at which spikes occur as an essential dimension in neural representations. We present a feature-linking model (FLM) that uses the timing of spikes to encode information. The first spiking time of FLM is applied to image enhancement, and the processing mechanisms are consistent with the human visual system. The enhancement algorithm achieves boosting the details while preserving the information of the input image. Experiments are conducted to demonstrate the effectiveness of the proposed method. Results show that the proposed method is effective.

scholarly journals The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

2012 ◽  
Vol 10 (3) ◽  
pp. 455-488 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon ◽  
Nicole Lemire
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Vector Bundles ◽  
Upper Bounds ◽  
Essential Dimension ◽  
Parabolic Structure ◽  
Moduli Stack

AbstractWe find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

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