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TitleUniversal associative envelopes of nonassociative triple systems.
Author(s) Hader A. Elgendy
TypeArticle in Journal
AbstractWe construct universal associative envelopes for the nonassociative triple systems arising from the trilinear operations of Bremner and Peresi applied to the 2-dimensional simple associative triple system. We use noncommutative Gröbner bases to determine monomial bases, structure constants, and centers of the universal envelopes. We show that the infinite dimensional envelopes are closely related to the down-up algebras of Benkart and Roby. For the finite dimensional envelopes, we determine the Wedderburn decompositions and classify the irreducible representations.
Keywords Gröbner bases, Representation theory, Triple systems, Universal associative enveloping algebras, Primary 17D99, Secondary 17C55, 17B35, 17A40
ISSN0092-7872; 1532-4125/e
URL http://www.tandfonline.com/doi/abs/10.1080/00927872.2012.749409#.VfA22lppF90
LanguageEnglish
JournalCommun. Algebra
Volume42
Number4
Pages1785--1810
PublisherTaylor & Francis, Philadelphia, PA
Year2014
Edition0
Translation No
Refereed No
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