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On quasigroups with the left loop property

A. Nourou Issa (2000)

Commentationes Mathematicae Universitatis Carolinae

Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.

On quasihomogeneous manifolds – via Brion-Luna-Vust theorem

Marco Andreatta, Jarosław A. Wiśniewski (2003)

Bollettino dell'Unione Matematica Italiana

We consider a smooth projective variety X on which a simple algebraic group G acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of G with the induced action of G on the normal bundle of a closed orbit of the action. We get effective results in case G = S L n and dim X 2 n - 2 .

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