1. Representations of simple anti-Jordan triple systems of matrices.
- Author
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Elgendy, Hader A.
- Subjects
- *
MATRICES (Mathematics) , *STEINER systems , *UNIVERSAL enveloping algebras , *DIMENSIONAL analysis , *INFINITY (Mathematics) - Abstract
We show that the universal associative envelope of the simple anti-Jordan triple system of all ( is even, ) matrices over an algebraically closed field of characteristic 0 is finite-dimensional. The monomial basis and the center of the universal envelope are determined. The explicit decomposition of the universal envelope into matrix algebras is given. The classification of finite-dimensional irreducible representations of an anti-Jordan triple system is obtained. The semi-simplicity of the universal envelope is shown. We also show that the universal associative envelope of the simple polarized anti-Jordan triple system of matrices is infinite-dimensional. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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