Preserving mixed skew Lie-Jordan-n-product on von Neumann algebra
Abstract
Abstract This work focuses on characterizing structure-preserving maps between factor von Neumann algebras with respect to a class of mixed skew Lie–Jordan $$n$$ n -products. Specifically, we consider expressions of the form $$ [A_1, A_2]_*\circ A_3 \circ \cdots \circ A_n, $$ [ A 1 , A 2 ] ∗ ∘ A 3 ∘ ⋯ ∘ A n , where each $$A_i \in \mathfrak {S}$$ A i ∈ S and $$\mathfrak {S}$$ S is a factor von Neumann algebra. Here, the skew Lie product is defined by $$[A_1, A_2]_*= A_1A_2 - A_2^*A_1$$ [ A 1 , A 2 ] ∗ = A 1 A 2 - A 2 ∗ A 1 , and the Jordan product by $$A_1 \circ A_2 = A_1A_2 + A_2A_1$$ A 1 ∘ A 2 = A 1 A 2 + A 2 A 1 . We prove that any map preserving these mixed products is necessarily a linear $$*$$ ∗ -isomorphism.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Operator Algebra Research
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Ricerche di Matematica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 75
- Issue
- 4
- Pages
- 1935–1949
- Publication date
- 13 April 2026
- Language
- EN
- Document type
- Book chapter