Universal Enveloping Algebras of Simple Symplectic Anti-Jordan Triple Systems

作者：Tvalavadze Marina^*

来源：Algebra Colloquium, 2015, 22(2): 281-292.

DOI：10.1142/S1005386715000255

• anti-Jordan triple systems
• universal enveloping algebras
• central elements
• PBW-bases

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 epsilon: 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).

• 出版日期2015-6