Alg\`ebres de Jordan et th\'eorie des invariants

TL;DR

This paper provides a unified description of invariant algebras associated with simple complex Euclidean Jordan algebras under a specific group action, focusing on cases where p is up to three.

Contribution

It offers a comprehensive analysis of invariant algebras C[pV]^G for simple Euclidean Jordan algebras, extending understanding of their structure for p ≤ 3.

Findings

Explicit descriptions of invariant algebras for p ≤ 3

Unified framework for different Jordan algebras

Insights into the structure of invariants under G

Abstract

If V is a simple complex euclidean Jordan algebra and G the subgroup of GL(V) fixing the determinant of V, we give a unified description of the invariant algebras C[pV]^G, for p not greater than three.