Enveloping Algebras of Filippov Algebras

DOI10.1081/AGB-120017349zbMath1025.17002MaRDI QIDQ4801402

Alexander P. Pozhidaev

Publication date: 7 April 2003

Published in: Communications in Algebra (Search for Journal in Brave)

zbMATH Keywords

\(n\)-Lie algebra\(n\)-ary algebraFilippov algebra

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) (n)-ary systems ((nge 3)) (20N15) Ternary compositions (17A40) Other (n)-ary compositions ((n ge 3)) (17A42)

Related Items (14)

Universal Associative Envelopes of (n+ 1)-Dimensionaln-Lie Algebras ⋮ On ID^∗-derivations of Filippov algebras ⋮ Representation theory of polyadic groups. ⋮ Poisson and Filippov superalgebras ⋮ Around the Hosszú-Gluskin theorem for \(n\)-ary groups. ⋮ Simple Poisson-Farkas algebras and ternary Filippov algebras ⋮ On Identities of a Ternary Quaternion Algebra ⋮ Alternating quaternary algebra structures on irreducible representations of \(\mathfrak{sl}_2(\mathbb C)\) ⋮ Binary Relations on Ternary Semihypergroups ⋮ Construction of \(n\)-ary \(F\)-polygroups. ⋮ ON SIMPLE FILIPPOV SUPERALGEBRAS OF TYPE A(n, n) ⋮ A Generalization ofn-Ary Algebraic Systems ⋮ Bi-Element Representations of Ternary Groups^# ⋮ Some properties of hyperideals in ternary semihypergroups

Cites Work

• Leibniz and Lie algebra structures for Nambu algebra
• On foundation of the generalized Nambu mechanics
• On an \(n\)-Lie algebra of Jacobians
• Simple quotient algebras and subalgebras of Jacobian algebras
• On Filippov algebroids and multiplicative Nambu-Poisson structures
• Generalized Hamiltonian Dynamics

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