Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

DOI10.14712/1213-7243.2015.188zbMath1438.17001arXiv1407.3810OpenAlexW2963523350MaRDI QIDQ2955949

Murray R. Bremner, Luiz Antonio Peresi, Sara Madariaga Merino

Publication date: 13 January 2017

Published in: Commentationes Mathematicae Universitatis Carolinae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.3810

zbMATH Keywords

idempotentsgroup algebrasymmetric groupcomputer algebrarepresentation theorypolynomial identitiesstandard tableauxoctonionsYoung diagramstwo-sided idealsWedderburn decompositionnonassociative algebramatrix unitsClifton's algorithm

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Representations of finite symmetric groups (20C30) Group rings (16S34) Identities, free Lie (super)algebras (17B01) Computational aspects of associative rings (general theory) (16Z05) Computational methods for problems pertaining to nonassociative rings and algebras (17-08) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Identities and free Jordan structures (17C05) Alternative rings (17D05) Composition algebras (17A75) Free nonassociative algebras (17A50) Software, source code, etc. for problems pertaining to nonassociative rings and algebras (17-04)

Related Items (7)

On tortkara triple systems ⋮ Higher polynomial identities for mutations of associative algebras ⋮ Identities of the algebra 𝕆⊗𝕆 ⋮ Associator dependent algebras and Koszul duality ⋮ Splitting of operations for alternative and Malcev structures ⋮ Special identities for comtrans algebras ⋮ Symmetrization of Jordan dialgebras

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