Algebras with involution and multiplicities bounded by a constant

Rizzo, Carla

doi:10.1016/j.jalgebra.2019.12.002

Cited by 5 publications

(1 citation statement)

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“…The presence of an anti-involution, not a guaranteed fact if the algebra is not commutative, leads to many interesting properties. For example, ideals of identities of a finitely generated algebra with involution coincide with ideals of identities for a finite dimensional algebra [24], and if an associative algebra with involution satisfies some polynomial identities, then the Grassmann envelope of the related superalgebra with superinvolution satisfies the same polynomial properties [1,23].…”

Section: Introductionmentioning

confidence: 99%

Deforming algebras with anti-involution via twisted associativity

Langlois-Rémillard

2021

Preprint

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This contribution introduces a framework to study a deformation of algebras with anti-involution. Starting with the observation that twisting the multiplication of such an algebra by its anti-involution generates a Hom-associative algebra of type II, it formulates the adequate modules theory over these algebras, and shows that there is a faithful functor from the category of finite-dimensional left modules of algebras with involution to finite-dimensional right modules of Hom-associative algebras of type II.

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Section: Introductionmentioning

confidence: 99%