Polynomial identities with involution, superinvolutions and the Grassmann envelope

Eli Aljadeff; Antonio Giambruno; Yakov Karasik

doi:10.1090/proc/13546

Polynomial identities with involution, superinvolutions and the Grassmann envelope

Eli Aljadeff^*, Antonio Giambruno, Yakov Karasik

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.

Original language	English
Pages (from-to)	1843-1857
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	5
DOIs	https://doi.org/10.1090/proc/13546
State	Published - 2017
Externally published	Yes

Keywords

Grassmann algebra
Involution
Polynomial identity
Superinvolution

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title = "Polynomial identities with involution, superinvolutions and the Grassmann envelope",

abstract = "Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.",

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AU - Aljadeff, Eli

AU - Giambruno, Antonio

AU - Karasik, Yakov

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N2 - Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.

AB - Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.

KW - Grassmann algebra

KW - Involution

KW - Polynomial identity

KW - Superinvolution

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Polynomial identities with involution, superinvolutions and the Grassmann envelope

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Keywords

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