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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).
Additional information
Funding
The first author was supported by the Discovery Grant Algebraic Operads from the Natural Sciences and Engineering Research Council of Canada (NSERC). The second author was supported by a Postdoctoral Fellowship from the Ministry of Higher Education of Egypt.