The Variety of Two-dimensional Algebras Over an Algebraically Closed Field

Kaygorodov, Ivan ; Volkov, Yury

Canadian journal of mathematics, Tome 71 (2019) no. 4, pp. 819-842

Résumé

The work is devoted to the variety of two-dimensional algebras over algebraically closed fields. First we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of certain algebra series in the variety of two-dimensional algebras. Finally, we apply our results to obtain analogous descriptions for the subvarieties of flexible and bicommutative algebras. In particular, we describe rigid algebras and irreducible components for these subvarieties.

Détail

DOI : 10.4153/S0008414X18000056

Mots-clés : two-dimensional algebras, orbit closure, degeneration, rigid algebra

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