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

Published electronically:
April 28, 2010

MathSciNet review:
2645047

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Abstract | References | Similar Articles | Additional Information

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:
http://dx.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.