Representations of simple anti-Jordan triple systems of m × n matrices

DOI10.1142/S0219498817500931zbMath1407.17006MaRDI QIDQ5739062

Hader A. Elgendy

Publication date: 2 June 2017

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

universal enveloping algebrasrepresentation theoryfree associative algebrasanti-Jordan triple systemsnoncommutative Gröbner-Shirshov bases

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Jordan structures associated with other structures (17C50) Ternary compositions (17A40)

Related Items (3)

Representations of the comtrans algebra of n × n matrices ⋮ Special identities for comtrans algebras ⋮ On the universal envelope of a Jordan triple system of n × n matrices

Cites Work

• Freudenthal gauge theory
• \(\mathcal N= 6\) superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The diamond lemma for ring theory
• The universal associative envelope of the anti-Jordan triple system of \(n\times n\) matrices
• Three-algebras and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>6</mml:mn></mml:math>Chern-Simons gauge theories
• Simple anti-jordan pairs¹
• Gröbner–Shirshov bases and their calculation
• Universal Enveloping Algebras of Simple Symplectic Anti-Jordan Triple Systems
• Universal Associative Envelopes of Nonassociative Triple Systems
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