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.
Aljadeff, E., Giambruno, A., Karasik, Y. (2017). Polynomial identities with involution, superinvolutions and the Grassmann envelope. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145(5), 1843-1857 [10.1090/proc/13546].
Polynomial identities with involution, superinvolutions and the Grassmann envelope
Giambruno, Antonino
;
2017-01-01
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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