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The Variety of Two-dimensional Algebras over an Algebraically Closed Field. / Kaygorodov, Ivan; Volkov, Yury.

In: Canadian Journal of Mathematics, Vol. 71, No. 4, 01.08.2019, p. 819-842.

Research output: Contribution to journal › Article › peer-review

Harvard

Kaygorodov, I & Volkov, Y 2019, 'The Variety of Two-dimensional Algebras over an Algebraically Closed Field', Canadian Journal of Mathematics, vol. 71, no. 4, pp. 819-842. https://doi.org/10.4153/S0008414X18000056

APA

Kaygorodov, I., & Volkov, Y. (2019). The Variety of Two-dimensional Algebras over an Algebraically Closed Field. Canadian Journal of Mathematics, 71(4), 819-842. https://doi.org/10.4153/S0008414X18000056

Vancouver

Kaygorodov I, Volkov Y. The Variety of Two-dimensional Algebras over an Algebraically Closed Field. Canadian Journal of Mathematics. 2019 Aug 1;71(4):819-842. https://doi.org/10.4153/S0008414X18000056

Author

Kaygorodov, Ivan ; Volkov, Yury. / The Variety of Two-dimensional Algebras over an Algebraically Closed Field. In: Canadian Journal of Mathematics. 2019 ; Vol. 71, No. 4. pp. 819-842.

BibTeX

@article{0ab30fc7462a45bbaa0e6f60710e308a,
title = "The Variety of Two-dimensional Algebras over an Algebraically Closed Field",
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.",
keywords = "Degeneration, Orbit closure, Rigid algebra., Two-dimensional algebras",
author = "Ivan Kaygorodov and Yury Volkov",
year = "2019",
month = aug,
day = "1",
doi = "10.4153/S0008414X18000056",
language = "English",
volume = "71",
pages = "819--842",
journal = "Canadian Journal of Mathematics",
issn = "0008-414X",
publisher = "Canadian Mathematical Society",
number = "4",

}

RIS

TY - JOUR

T1 - The Variety of Two-dimensional Algebras over an Algebraically Closed Field

AU - Kaygorodov, Ivan

AU - Volkov, Yury

PY - 2019/8/1

Y1 - 2019/8/1

N2 - 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.

AB - 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.

KW - Degeneration

KW - Orbit closure

KW - Rigid algebra.

KW - Two-dimensional algebras

UR - http://www.scopus.com/inward/record.url?scp=85069526717&partnerID=8YFLogxK

U2 - 10.4153/S0008414X18000056

DO - 10.4153/S0008414X18000056

M3 - Article

AN - SCOPUS:85069526717

VL - 71

SP - 819

EP - 842

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

SN - 0008-414X

IS - 4

ER -

ID: 43942679