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Polynomial identities with involution, superinvolutions and the Grassmann envelope


Authors: Eli Aljadeff, Antonio Giambruno and Yakov Karasik
Journal: Proc. Amer. Math. Soc. 145 (2017), 1843-1857
MSC (2010): Primary 16R10, 16R50; Secondary 16W10
DOI: https://doi.org/10.1090/proc/13546
Published electronically: January 11, 2017
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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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Additional Information

Eli Aljadeff
Affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
Email: aljadeff@tx.technion.ac.il

Antonio Giambruno
Affiliation: Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy
Email: antonio.giambruno@unipa.it

Yakov Karasik
Affiliation: Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
Email: yaakov@tx.technion.ac.il

DOI: https://doi.org/10.1090/proc/13546
Keywords: Polynomial identity, involution, superinvolution, Grassmann algebra
Received by editor(s): June 12, 2016
Published electronically: January 11, 2017
Additional Notes: The first author was partially supported by the ISRAEL SCIENCE FOUNDATION(grant No. 1017/12). The second author was partially supported by GNSAGA of INDAM
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2017 American Mathematical Society

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