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arXiv · 2402.06909

Noncommutative Poisson structure and invariants of matrices

Farkhod Eshmatov·Xabier García-Martínez·Rustam Turdibaev
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Abstract

We introduce a novel approach that employs techniques from noncommutative Poisson geometry to comprehend the algebra of invariants of two $n\times n$ matrices. We entirely solve the open problem of computing the algebra of invariants of two $4 \times 4$ matrices. As an application, we derive the complete description of the invariant commuting variety of $4 \times 4$ matrices and the fourth Calogero-Moser space.

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Farkhod Eshmatov, Xabier García-Martínez, Rustam Turdibaev. 2024-02-10. Noncommutative Poisson structure and invariants of matrices. https://arxiv.org/abs/2402.06909

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