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

By Ivan Kaygorodov, Y. Volkov. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2017

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Abstract 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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

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