Assosymmetric algebras under jordan product
A.S. Dzhumadil'daev
TL;DR
This paper investigates assosymmetric algebras under Jordan product, proving they are Lie triple and exploring the properties of special Lie triple algebras, including the validity of Glennie identity.
Contribution
It establishes that assosymmetric algebras under Jordan product are Lie triple and analyzes the Glennie identity's applicability to special Lie triple algebras.
Findings
Assosymmetric algebras under Jordan product are Lie triple.
Glennie identity holds for special Lie triple algebras.
Not all Lie triple algebras satisfy Glennie identity.
Abstract
We prove that assosymmetric algebras under Jordan product are Lie triple. A Lie triple algebra is called special if it is isomorphic to a subalgebra of some plus-assosymmetric algebra. We establish that Glennie identitiy is valid for special Lie triple algebras, but not for all Lie triple algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research