Geodesic
The Variety of Two-dimensional Algebras Over an Algebraically Closed Field
Canadian journal of mathematics, Tome 71 (2019) no. 4, pp. 819-842

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DOI

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.
DOI : 10.4153/S0008414X18000056
Mots-clés : two-dimensional algebras, orbit closure, degeneration, rigid algebra 
Kaygorodov, Ivan; Volkov, Yury. The Variety of Two-dimensional Algebras Over an Algebraically Closed Field. Canadian journal of mathematics, Tome 71 (2019) no. 4, pp. 819-842. doi: 10.4153/S0008414X18000056
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     title = {The {Variety} of {Two-dimensional} {Algebras} {Over} an {Algebraically} {Closed} {Field}},
     journal = {Canadian journal of mathematics},
     pages = {819--842},
     year = {2019},
     volume = {71},
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