A Structure Theory for Jordan Algebras

1947 ◽  
Vol 48 (3) ◽  
pp. 546 ◽  
Author(s):  
A. A. Albert
Keyword(s):  
Jordan Algebras ◽  
Structure Theory

scholarly journals Automorphism Groups of Jordan Algebras

1968 ◽  
Vol 32 ◽  
pp. 227-235
Author(s):  
E. Ray Bobo
Keyword(s):  
Vector Space ◽  
Automorphism Groups ◽  
Infinite Family ◽  
Jordan Algebras ◽  
Structure Theory ◽  
Important Class ◽  
Natural Basis ◽  
Generators And Relations ◽  
Characteristic Two ◽  
Central Simple

In his development of a structure theory for Jordan algebras of characteristic two, E.C. Paige [1] introduces an important class of central simple Jordan algebras S[2n], It is the purpose of this paper to completely determine the automorphism groups of the algebras S[2n]. The automorphisms will be represented as matrices operating on a natural basis for the underlying vector space of the algebra. Using this characterization, generators and relations will be obtained for each of the automorphism groups. In this way, we will produce an infinite family of finite 2-groups.

Combining First-Principles and Data Modeling for the Accurate Prediction of the Refractive Index of Organic Polymers

2017 ◽  
Author(s):  
Mohammad Atif Faiz Afzal ◽  
Chong Cheng ◽  
Johannes Hachmann
Keyword(s):  
First Principles ◽  
Data Modeling ◽  
Accurate Prediction ◽  
Index Of Refraction ◽  
Structure Theory ◽  
Organic Polymers ◽  
Number Density ◽  
Lorenz Equation ◽  
In Silico Studies ◽  
Wide Range

Organic materials with a high index of refraction (RI) are attracting considerable interest due to their potential application in optic and optoelectronic devices. However, most of these applications require an RI value of 1.7 or larger, while typical carbon-based polymers only exhibit values in the range of 1.3–1.5. This paper introduces an efficient computational protocol for the accurate prediction of RI values in polymers to facilitate in silico studies that an guide the discovery and design of next-generation high-RI materials. Our protocol is based on the Lorentz-Lorenz equation and is parametrized by the polarizability and number density values of a given candidate compound. In the proposed scheme, we compute the former using first-principles electronic structure theory and the latter using an approximation based on van der Waals volumes. The critical parameter in the number density approximation is the packing fraction of the bulk polymer, for which we have devised a machine learning model. We demonstrate the performance of the proposed RI protocol by testing its predictions against the experimentally known RI values of 112 optical polymers. Our approach to combine first-principles and data modeling emerges as both a successful and highly economical path to determining the RI values for a wide range of organic polymers.

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