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

  • Ivan Kaygorodov (a1) and Yury Volkov (a2)

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.

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Copyright

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The work was supported by FAPESP 14/24519-8; RFBR 17-51-04004; the President’s Program “Support of Young Russian Scientists” (grant MK-1378.2017.1).

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References

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

  • Ivan Kaygorodov (a1) and Yury Volkov (a2)

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