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Classification of contraction algebras and pre-Lie algebras associated to braces and trusses

Research output: Contribution to Journal/Magazine › Journal article

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Classification of contraction algebras and pre-Lie algebras associated to braces and trusses. / Iyudu, Natalia.
In: arXiv.org, 13.08.2020.

Research output: Contribution to Journal/Magazine › Journal article

Harvard

Iyudu, N 2020, 'Classification of contraction algebras and pre-Lie algebras associated to braces and trusses', arXiv.org.

APA

Iyudu, N. (2020). Classification of contraction algebras and pre-Lie algebras associated to braces and trusses. arXiv.org.

Vancouver

Iyudu N. Classification of contraction algebras and pre-Lie algebras associated to braces and trusses. arXiv.org. 2020 Aug 13.

Author

Iyudu, Natalia. / Classification of contraction algebras and pre-Lie algebras associated to braces and trusses. In: arXiv.org. 2020.

Bibtex

@article{c986fd3ca5e24b4a9a95c74d1c5d6594,
title = "Classification of contraction algebras and pre-Lie algebras associated to braces and trusses",
abstract = " We develop tools for classification of contraction algebras and apply these to solve the problem on classification up to isomorphism of 8 and 9 dimensional algebras corresponding to 3-fold flops. We prove that there is only one up to isomorphism contraction algebra of dimension 8, and two algebras of dimension 9. The formulae for the dimension of algebra, depending on the type of the potential are obtained. In the second part of the paper we show that associated graded structure to brace and truss with appropriate descending ideal filtration is pre-Lie. ",
keywords = "math.RA, math.AG, math.GR, math.RT",
author = "Natalia Iyudu",
note = "19 pages",
year = "2020",
month = aug,
day = "13",
language = "Undefined/Unknown",
journal = "arXiv.org",

}

RIS

TY - JOUR

T1 - Classification of contraction algebras and pre-Lie algebras associated to braces and trusses

AU - Iyudu, Natalia

N1 - 19 pages

PY - 2020/8/13

Y1 - 2020/8/13

N2 - We develop tools for classification of contraction algebras and apply these to solve the problem on classification up to isomorphism of 8 and 9 dimensional algebras corresponding to 3-fold flops. We prove that there is only one up to isomorphism contraction algebra of dimension 8, and two algebras of dimension 9. The formulae for the dimension of algebra, depending on the type of the potential are obtained. In the second part of the paper we show that associated graded structure to brace and truss with appropriate descending ideal filtration is pre-Lie.

AB - We develop tools for classification of contraction algebras and apply these to solve the problem on classification up to isomorphism of 8 and 9 dimensional algebras corresponding to 3-fold flops. We prove that there is only one up to isomorphism contraction algebra of dimension 8, and two algebras of dimension 9. The formulae for the dimension of algebra, depending on the type of the potential are obtained. In the second part of the paper we show that associated graded structure to brace and truss with appropriate descending ideal filtration is pre-Lie.

KW - math.RA

KW - math.AG

KW - math.GR

KW - math.RT

M3 - Journal article

JO - arXiv.org

JF - arXiv.org

ER -