Structure of Zariski-closed algebras

Details Structure of Zariski-closed algebras Structure of Zariski-closed algebras

2011-09-22

arxiv.org/abs/1109.4912v1

Trans. Amer. Math. Soc, Vol. 362(9), 4695-4734, (2010)

Mathematics

Rings and Algebras

40 pages

Scientific paper

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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