Details:
Title  The universal associative envelope of the antiJordan triple system of matrices  Author(s)  Hader A. Elgendy  Type  Article in Journal  Abstract  Abstract We show that the universal associative enveloping algebra of the simple antiJordan triple system of all n × n matrices ( n ⩾ 2 ) over an algebraically closed field of characteristic 0 is finitedimensional. 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 finitedimensional irreducible representations of the simple antiJordan triple system, and show that the universal envelope is semisimple. We also provide an example to show that the universal enveloping algebras of antiJordan triple systems are not necessary to be finitedimensional.  Keywords  AntiJordan triple systems, Universal Representation theory  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869313001191 
Language  English  Journal  Journal of Algebra  Volume  383  Pages  1  28  Year  2013  Edition  0  Translation 
No  Refereed 
No 
