Noncommutative Poisson structure and invariants of matrices
Copyright policy )Noncommutative Poisson structure and invariants of matrices
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.
Noncommutative algebraic geometry, commuting variety, Calogero-Moser space, Rings and Algebras (math.RA), Trace rings and invariant theory (associative rings and algebras), FOS: Mathematics, 16R30, 16S38, 14A22, 13A50, noncommutative Poisson structure, Mathematics - Rings and Algebras, Rings arising from noncommutative algebraic geometry, Actions of groups on commutative rings; invariant theory, invariant theory
Noncommutative algebraic geometry, commuting variety, Calogero-Moser space, Rings and Algebras (math.RA), Trace rings and invariant theory (associative rings and algebras), FOS: Mathematics, 16R30, 16S38, 14A22, 13A50, noncommutative Poisson structure, Mathematics - Rings and Algebras, Rings arising from noncommutative algebraic geometry, Actions of groups on commutative rings; invariant theory, invariant theory
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