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Content archived on 2024-05-29

Quasigroups, loops and related binary systems on algebraic manifolds

Objective

The concept of quasigroups is the non- associative generalization of the concept of groups. Since the 1930's, different categories (finite, topological, analytic) of quasigroups were intensively studied. In this project, we intend to investigate algebraic quasigroups and related geometric and group theoretical structures. The adjective algebraic is meant in the sense of algebraic geometry, that is, we assume that the underlying set Q of the quasigroup is an algebraic variety and the multiplication and its in verses are regular morphisms for Q×Q to Q.

In our investigations, we will concentrate on the following problems: Factors of algebraic quasigroups; algebraic quasigroups and algebraic transformation groups; non regular algebraic quasigroups; the geometry of algebraic quasigroups. Our main tool is to collect information on the transformation groups generated by left and right multiplications of the quasigroup or special symmetries of the associated 3-net.

Fields of science (EuroSciVoc)

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Keywords

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Topic(s)

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Call for proposal

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FP6-2005-MOBILITY-5
See other projects for this call

Funding Scheme

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EIF - Marie Curie actions-Intra-European Fellowships

Coordinator

BAYERISCHE JULIUS-MAXIMILIANS-UNIVERSITAET WUERZBURG
EU contribution
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Total cost

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