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.
2010 Mathematics Subject Classifications:
Acknowledgments
We thank Vladimir Dotsenko for providing us with the counter-example in Question 5.9.
Disclosure statement
No potential conflict of interest was reported by the author(s).