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Vinberg's T-Algebras. From Exceptional Periodicity to Black Hole Entropy
by Alessio Marrani
This Submission thread is now published as
|Authors (as registered SciPost users):||Alessio Marrani|
|Preprint Link:||scipost_202306_00034v2 (pdf)|
|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)|
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.
Published as SciPost Phys. Proc. 14, 035 (2023)
Author comments upon resubmission
I have implemented all amendments pointed out by the Referee, and also completed/updated the bibliography.
Submission & Refereeing History
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