On the structure of split non-commutative Poisson algebras

DOI10.1080/03081087.2012.661428zbMath1266.17012OpenAlexW2092023624MaRDI QIDQ5200318

Antonio Jesús Calderón Martín

Publication date: 5 November 2012

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2012.661428

zbMATH Keywords

structure theoryconnection of rootssplit algebraPoisson noncommutative algebra

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Poisson algebras (17B63)

Related Items (15)

Arbitrary algebras with a multiplicative basis ⋮ A Note on Strongly Graded Lie Algebras ⋮ RETRACTED ARTICLE: Split Malcev-Poisson-Jordan algebras ⋮ Fine decompositions of algebraic systems induced by bases ⋮ On extended graded Poisson algebras ⋮ On split Leibniz superalgebras ⋮ Poisson color algebras of arbitrary degree ⋮ Arbitrary triple systems admitting a multiplicative basis ⋮ Non-commutative Poisson Algebras Admitting a Multiplicative Basis ⋮ Split Lie–Rinehart algebras ⋮ The global extension problem, crossed products and co-flag non-commutative Poisson algebras ⋮ Strongly Split Poisson Algebras ⋮ On split Malcev Poisson algebras ⋮ (ANTI)COMMUTATIVE ALGEBRAS WITH A MULTIPLICATIVE BASIS ⋮ A second Wedderburn-type theorem for some classes of linearly structured matrices

Cites Work

• Projective geometry from Poisson algebras
• On the structure of split Lie color algebras
• Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras
• On split Lie algebras with symmetric root systems
• Finite-dimensional non-commutative Poisson algebras
• Non-commutative Poisson algebra structures on affine Kac-Moody algebras
• The structure of locally finite split Lie algebras
• FINITE-DIMENSIONAL NON-COMMUTATIVE POISSON ALGEBRAS. II

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