Structure of Zariski-closed algebras

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The objective of this paper is to describe the structure of Zariskiclosed 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.

Original languageEnglish
Pages (from-to)4695-4734
Number of pages40
JournalTransactions of the American Mathematical Society
Issue number9
StatePublished - Sep 2010


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