Universal differential calculus on ternary algebras

Abstract

General concept of ternary algebras is introduced in this article, along with several examples of its realization. Universal envelope of such algebras is defined, as well as the concept of tri-modules over ternary algebras. The universal differential calculus on these structures is then defined and its basic properties investigated.

References in corpus (6)

• The cubic chessboard
• On the q-analog of homological algebra
• Universal $q$-differential calculus and $q$-analog of homological algebra
• n-ary Lie and Associative Algebras
• Bi-element representations of ternary groups
• On the $n$-ary algebras, semigroups and their universal covers

Cited by in corpus (23)

• n-ary algebras: a review with applications
• Generalization of n-ary Nambu algebras and beyond
• Approximate Homomorphisms of Ternary Semigroups
• Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
• Unusual area-law violation in random inhomogeneous systems
• On the ternary complex analysis and its applications
• Satbility of Ternary Homomorphisms via Generalized Jensen Equation
• Hopf algebras for ternary algebras
• Semiheaps and Ternary Algebras in Quantum Mechanics Revisited
• Ternary algebras and groups
• The partially alternating ternary sum in an associative dialgebra
• Arity shape of polyadic algebraic structures
• Notes on Cohomologies of Ternary Algebras of Associative Type
• Some Results on Cubic and Higher Order Extensions of the Poincaré Algebra
• Stability of homomorphisms and derivations in $C^{\ast }$-ternary algebras
• Stability of the Jensen--type functional equation in ternary Banach algebras: An alternative fixed point approach
• Stability of ternary Jordan homomorphisms and derivations associated to the generalized Jensen equation
• (Co)associative $3$-ary (co)algebras and infinitesimal bialgebras: construction and main properties
• On approximate ternary m-derivations and $\sigma$-homomorphisms
• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
• Para-associative Algebroids
• Hom-coassociative ternary coalgebras and infinitesimal bialgebras
• A Multiparametric Quantum Superspace and Its Logarithmic Extension