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Journal of Lie Theory 18 (2008), No. 2, 375--382
Copyright Heldermann Verlag 2008

Right Ideals in Non-Associative Universal Enveloping Algebras of Lie Triple Systems

José M. Pérez-Izquierdo
Dpto. Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain

We prove that the only proper right ideal of the universal enveloping algebra of a finite-dimensional central simple Lie triple system over a field of characteristic zero is its augmentation ideal. This provides new series of infinite-dimensional simple non-associative algebras strongly connected with Hopf algebras and geometry.

Keywords: Lie triple systems, Sabinin algebras, universal enveloping algebras, nonassociative bialgebras.

MSC: 17A40

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