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The algebraic and geometric classification of associative algebras of dimension five

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Abstract

The scheme Alg5 of associative, unitary algebra structures on k5, k an algebraically closed field with char (k)≠2 is investigated. We establish the list of GL5-orbits on Alg5 under the action of structural transport. The numberalg5 of irreducible components of Alg5 is 10; a list of generic structures is included. We exhibit upper and lower bounds for the asymptotic behaviour of the numberalgn.

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  1. Mathematisches Institut, Universität Zürich, Freiestrasse 36, CH-8032, Zürich

    Guerino Mazzola

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  1. Guerino Mazzola
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Mazzola, G. The algebraic and geometric classification of associative algebras of dimension five. Manuscripta Math 27, 81–101 (1979). https://doi.org/10.1007/BF01297739

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  • DOI: https://doi.org/10.1007/BF01297739

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