Invariant Nonassociative Algebra Structures on Irreducible Representations of Simple Lie Algebras

DOI10.1080/10586458.2004.10504536zbMath1139.17300OpenAlexW2087036650WikidataQ115295943 ScholiaQ115295943MaRDI QIDQ4828775

Irvin Roy Hentzel, Murray R. Bremner

Publication date: 26 November 2004

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1090350937

zbMATH Keywords

representationssimple Lie algebraspolynomial identitiescomputational linear algebraanticommutative algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Computational methods for problems pertaining to nonassociative rings and algebras (17-08) Nonassociative algebras satisfying other identities (17A30) Software, source code, etc. for problems pertaining to nonassociative rings and algebras (17-04)

Related Items (8)

Ternary analogues of Lie and Malcev algebras ⋮ A polynomial identity for the bilinear operation in Lie–Yamaguti algebras ⋮ Lie structures and chain ideal lattices ⋮ Reductive homogeneous spaces of the compact Lie group \(G_2\) ⋮ Duality between p-groups with three characteristic subgroups and semisimple anti-commutative algebras ⋮ The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra ⋮ Alternating quaternary algebra structures on irreducible representations of \(\mathfrak{sl}_2(\mathbb C)\) ⋮ Lie-Yamaguti algebras related to \(\mathfrak g_2\)

Uses Software

• Maple
• LiE

Cites Work

• Certaines algèbres non associatives simples définies par la transvection des formes binaires.

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