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- W4313242110 abstract "Let $mathcal{J}_{field}$ be the Jordan triple system of all $p times q$ ($pneq q$; $p,q >1)$ rectangular matrices over a field $field$ of characteristic 0 with the triple product ${x,y,z}= x y^t z+ z y^t x $, where $y^t$ is the transpose of $y$. We study the universal associative envelope $mathcal{U}(mathcal{J}_{field})$ of $mathcal{J}_{field}$ and show that $mathcal{U}(mathcal{J}_{field}) cong M_{p+q times p+q}(field)$, where $M_{p+qtimes p+q} (field)$ is the ordinary associative algebra of all $(p+q) times (p+q)$ matrices over $field$. It follows that there exists only one nontrivial irreducible representation of $mathcal{J}_{field}$. The center of $mathcal{U}(mathcal{J}_{field})$ is deduced." @default.
- W4313242110 created "2023-01-06" @default.
- W4313242110 creator A5029050596 @default.
- W4313242110 date "2023-01-09" @default.
- W4313242110 modified "2023-10-18" @default.
- W4313242110 title "On the irreducible representations of the Jordan triple system of $p times q$ matrices" @default.
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- W4313242110 doi "https://doi.org/10.24330/ieja.1226320" @default.
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