TL;DR
This paper introduces Poisson triple systems, a new algebraic structure with three trilinear operations, and explores their properties, including the existence of a universal enveloping algebra and operadic aspects.
Contribution
It defines Poisson triple systems, proves the existence of their universal enveloping Poisson algebra, and discusses their operadic structure, advancing algebraic theory.
Findings
Poisson triple systems are vector spaces with 3 trilinear operations satisfying 9 polynomial identities.
Every Poisson triple system has a universal enveloping Poisson algebra.
Operadic aspects of Poisson triple systems are briefly discussed.
Abstract
We introduce Poisson triple systems, which are vector spaces with 3 trilinear operations satisfying 9 polynomial identities of degree 5. We show that every Poisson triple system has a universal enveloping Poisson algebra. Finally, we briefly discuss operadic aspects of Poisson triple systems.
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