Jordan algebras, exceptional groups, and Bhargava composition
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TL;DR: In this paper, an integral Freudenthal construction relating Jordan algebras and exceptional algebraic groups is proposed, which is related to higher composition laws of M. Bhargava in number theory.
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About: This article is published in Journal of Algebra. The article was published on 15 Aug 2007. and is currently open access. The article focuses on the topics: Freudenthal magic square & Jordan algebra.
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Citations
Non-Linear Invariance of Black Hole Entropy
Alessio Marrani
- 16 Oct 2017
TL;DR: Freudenthal duality is an anti-involutive, non-linear map acting on symplectic spaces as discussed by the authors, which holds in four-dimensional Maxwell-Einstein theories coupled to a nonlinear sigma model of scalar fields.
Albert algebras over $\mathbb {Z}$ and other rings
TL;DR: In this paper , the authors studied Albert algebras over an arbitrary base ring R, with particular attention to the case that R is a field of characteristic different from 2 and 3.
3
Peccei-Quinn Transformations and Black Holes : Orbit Transmutations and Entanglement Generation
TL;DR: In this paper, the Peccei-Quinn symplectic transformations are considered in the context of the transition from one U-duality orbit to another, or from an element of the Freudenthal Triple System with a definite rank to another one.
3
References
•Book
Octonions, Jordan Algebras and Exceptional Groups
Tonny A. Springer,Ferdinand D. Veldkamp +1 more
- 16 May 2000
TL;DR: The 1963 Gottingen notes of T. A. Springer are well-known in the field but have been unavailable for some time as mentioned in this paper, and they are completely updated and revised.
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