Universal Enveloping Algebras of Simple Symplectic Anti-Jordan Triple Systems
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Abstract
In this work we are concerned with the universal associative envelope of a finite-dimensional simple symplectic anti-Jordan triple system (AJTS). We prove that if 𝕋 is a triple system as above, then there exists an associative algebra U(𝕋) and an injective homomorphism ε : 𝕋 → U(𝕋), where U(𝕋) is an AJTS under the triple product defined by (a,b,c) = abc - cba. Moreover, U(𝕋) is a universal object with respect to such homomorphisms. We explicitly determine the PBW-basis of U(𝕋), the center Z(U(𝕋)) and the Gelfand-Kirillov dimension of U(𝕋).
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