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Structure of Zariski-closed algebras


Authors: Alexei Belov-Kanel, Louis Rowen and Uzi Vishne
Journal: Trans. Amer. Math. Soc. 362 (2010), 4695-4734
MSC (2010): Primary 16G99
DOI: https://doi.org/10.1090/S0002-9947-10-04993-7
Published electronically: April 28, 2010
MathSciNet review: 2645047
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Abstract: The objective of this paper is to describe the structure of Zariski-closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a version of Wedderburn's principal theorem as well as a more explicit description using representations, in terms of ``gluing'' in Wedderburn components. Finally, we construct ``generic'' Zariski-closed algebras, whose description is considerably more complicated than the description of generic algebra of finite dimensional algebras.

Special attention is given to infinite dimensional algebras over finite fields.


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Additional Information

Alexei Belov-Kanel
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
Email: belova@macs.biu.ac.il

Louis Rowen
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
Email: rowen@macs.biu.ac.il

Uzi Vishne
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
Email: vishne@macs.biu.ac.il

DOI: https://doi.org/10.1090/S0002-9947-10-04993-7
Received by editor(s): September 22, 2008
Published electronically: April 28, 2010
Additional Notes: This research was supported by the Israel Science Foundation, grant #1178/06.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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