Artículo de revista
Universal Poisson Envelope for Binary-Lie Algebras
Fecha
2013Registro en:
Communications in Algebra, Volumen 41, Issue 5, 2018, Pages 1781-1789
00927872
15324125
10.1080/00927872.2011.651757
Autor
Arenas, Manuel
Arenas Carmona, Luis
Institución
Resumen
In this article the universal Poisson enveloping algebra for a binary-Lie algebra is constructed. Taking a basis B{double-struck} of a binary-Lie algebra B, we consider the symmetric algebra S(B) of polynomials in the elements of B{double-struck}. We consider two products in S(B), the usual product of polynomials fg and the braces {f, g}, defined by the product in B and the Leibniz rule. This algebra is a general Poisson algebra. We find an ideal I of S(B) such that the factor algebra S(B)/I is the universal Poisson envelope of B. We provide some examples of this construction for known binary-Lie algebras. © 2013 Copyright Taylor and Francis Group, LLC.