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Vinberg's T-Algebras. From Exceptional Periodicity to Black Hole Entropy

by Alessio Marrani

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Authors (as registered SciPost users): Alessio Marrani
Submission information
Preprint Link: scipost_202306_00034v2  (pdf)
Date accepted: 2023-08-29
Date submitted: 2023-08-19 18:21
Submitted by: Marrani, Alessio
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


We introduce the so-called Magic Star (MS) projection within the root lattice of finite-dimensional exceptional Lie algebras, and relate it to rank-3 simple and semi-simple Jordan algebras. By relying on the Bott periodicity of reality and conjugacy properties of spinor representations, we present the so-called Exceptional Periodicity (EP) algebras, which are finite-dimensional algebras, violating the Jacobi identity, and providing an alternative with respect to Kac-Moody infinite-dimensional Lie algebras. Remarkably, also EP algebras can be characterized in terms of a MS projection, exploiting special Vinberg T-algebras, a class of generalized Hermitian matrix algebras introduced by Vinberg in the ’60s within his theory of homogeneous convex cones. As physical applications, we highlight the role of the invariant norm of special Vinberg T-algebras in Maxwell-Einstein-scalar theories in 5 space-time dimensions, in which the Bekenstein-Hawking entropy of extremal black strings can be expressed in terms of the cubic polynomial norm of the T-algebras.

Author comments upon resubmission

I thank the Referee for her/his remarks and constructive criticism.
I have implemented all amendments pointed out by the Referee, and also completed/updated the bibliography.

Published as SciPost Phys. Proc. 14, 035 (2023)

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