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

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Autor(es):	Kaygorodov, Ivan ^[1] ; Volkov, Yury ^[2] Número total de Autores: 2
Afiliação do(s) autor(es):	^[1] Univ Fed ABC, CMCC, Santo Andre - Brazil ^[2] St Petersburg State Univ, St Petersburg - Russia Número total de Afiliações: 2
Tipo de documento:	Artigo Científico
Fonte:	CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES; v. 71, n. 4, p. 819-842, AUG 2019.
Citações Web of Science:	7
Resumo
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. (AU)

Processo FAPESP:	14/24519-8 - Derivações gerais de álgebras e superálgebras não associativas
Beneficiário:	Ivan Kaygorodov
Modalidade de apoio:	Auxílio à Pesquisa - Regular