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TitleThe universal associative envelope of the anti-Jordan triple system of matrices
Author(s) Hader A. Elgendy
TypeArticle in Journal
AbstractAbstract We show that the universal associative enveloping algebra of the simple anti-Jordan triple system of all n × n matrices ( n ⩾ 2 ) over an algebraically closed field of characteristic 0 is finite-dimensional. We investigate the structure of the universal envelope and focus on the monomial basis, the structure constants, and the center. We explicitly determine the decomposition of the universal envelope into matrix algebras. We classify all finite-dimensional irreducible representations of the simple anti-Jordan triple system, and show that the universal envelope is semisimple. We also provide an example to show that the universal enveloping algebras of anti-Jordan triple systems are not necessary to be finite-dimensional.
KeywordsAnti-Jordan triple systems, Universal Representation theory
URL http://www.sciencedirect.com/science/article/pii/S0021869313001191
JournalJournal of Algebra
Pages1 - 28
Translation No
Refereed No