2017/01/31 by Ivan Kaygorodov, Yury Volkov
Mathematics · #math.RA
paper · pdf · doi:10.4153/s0008414x18000056
arxiv created 2019/04/01 · arxiv updated 2020/04/03
The work is devoted to the variety of 2-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the variety under consideration. 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.