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

Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)

Commentationes Mathematicae Universitatis Carolinae

This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra 𝔽 S n of the symmetric group S n over a field 𝔽 of characteristic 0 (or p > n ). The goal is to obtain a constructive version of the isomorphism ψ : λ M d λ ( 𝔽 ) 𝔽 S n where λ is a partition of n and d λ counts the standard tableaux of shape λ ....

Subalgebras of finite codimension in symplectic Lie algebra

Mohammed Benalili, Abdelkader Boucherif (1999)

Archivum Mathematicum

Subalgebras of germs of vector fields leaving 0 fixed in R 2 n , of finite codimension in symplectic Lie algebra contain the ideal of germs infinitely flat at 0 . We give an application.

Subloops of sedenions

Benard M. Kivunge, Jonathan D. H Smith (2004)

Commentationes Mathematicae Universitatis Carolinae

This note investigates sedenion multiplication from the standpoint of loop theory. New two-sided loops are obtained within the version of the sedenions introduced by the second author. Conditions are given for the satisfaction of standard loop-theoretical identities within these loops.

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