Transposed Poisson structures on the Lie algebra of upper triangular matrices

DOI10.4171/pm/2120arXiv2305.00727OpenAlexW4391804918MaRDI QIDQ6203854

Mykola Khrypchenko, I. B. Kaĭgorodov

Publication date: 8 April 2024

Published in: Portugaliae Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.00727

zbMATH Keywords

\(\delta\)-derivationtransposed Poisson algebraupper triangular matrix Lie algebrafull matrix Lie algebra

Mathematics Subject Classification ID

Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40) Poisson algebras (17B63) Nonassociative algebras satisfying other identities (17A30) Matrix Lie algebras (15B30)

Cites Work

• Commutativity preserving linear maps and Lie automorphisms of triangular matrix algebras
• On \(\delta\)-derivations of Lie algebras
• \(\frac12\)-derivations of Lie algebras and transposed Poisson algebras
• Transposed Poisson structures on Block Lie algebras and superalgebras
• Poisson structures for canonical algebras
• Quiver Poisson algebras
• Poisson structures on finitary incidence algebras
• The algebraic and geometric classification of transposed Poisson algebras
• Transposed Poisson structures on Witt type algebras
• Transposed Poisson structures on Galilean and solvable Lie algebras
• -(bi)derivations and transposed Poisson algebra structures on Lie algebras
• Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras
• Transposed Poisson structures
• Transposed Poisson structures on generalized Witt algebras and Block Lie algebras
• On the simple transposed Poisson algebras and Jordan superalgebras

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