Verbal width in the Nottingham group and related Lie algebras

Jorge Martinez Carracedo; Consuelo Martinez Lopez

doi:10.1016/j.jalgebra.2021.02.003

Verbal width in the Nottingham group and related Lie algebras

Jorge Martinez Carracedo, Consuelo Martinez Lopez

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Abstract

In [1], B. Klopsch proved that the Nottingham group over a finite field is verballyelliptic. We prove a similar result for fields of zero characteristic. We also provethat the Virasoro Lie algebra and some its subalgebras are polynomially elliptic

Original language	English
Pages (from-to)	316-326
Number of pages	11
Journal	Journal of Algebra
Volume	574
DOIs	https://doi.org/10.1016/j.jalgebra.2021.02.003
Publication status	Published (in print/issue) - 4 Feb 2021

Bibliographical note

Funding Information:
Authors are grateful to the referee who provided useful comments.
This work has been partially supported by the Government of Spain through the
project M T M 2017−83506−C2−2−P and by the Principado de Asturias through the project FC−GRUPIN−IDI/2018/000193.

Publisher Copyright:
© 2021 Elsevier Inc.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

Group
Lower Central Series
Graded Lie algebra
Nottingham group
Virasoro Algebra
Witt Algebra
Verbal Width
Ellipticity

Access to Document

10.1016/j.jalgebra.2021.02.003Licence: CC BY-ND

Journal_of_Algebra_Nottingham_GroupAuthor Accepted Manuscript, 349 KBLicence: CC BY-ND

https://www.sciencedirect.com/science/article/pii/S0021869321000673Licence: CC BY-ND

Cite this

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abstract = "In [1], B. Klopsch proved that the Nottingham group over a finite field is verballyelliptic. We prove a similar result for fields of zero characteristic. We also provethat the Virasoro Lie algebra and some its subalgebras are polynomially elliptic",

keywords = "Group, Lower Central Series, Graded Lie algebra, Nottingham group, Virasoro Algebra, Witt Algebra, Verbal Width, Ellipticity",

author = "{Martinez Carracedo}, Jorge and {Martinez Lopez}, Consuelo",

note = "Funding Information: Authors are grateful to the referee who provided useful comments. This work has been partially supported by the Government of Spain through the project M T M 2017−83506−C2−2−P and by the Principado de Asturias through the project FC−GRUPIN−IDI/2018/000193. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

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AU - Martinez Lopez, Consuelo

N1 - Funding Information: Authors are grateful to the referee who provided useful comments. This work has been partially supported by the Government of Spain through the project M T M 2017−83506−C2−2−P and by the Principado de Asturias through the project FC−GRUPIN−IDI/2018/000193. Publisher Copyright: © 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

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N2 - In [1], B. Klopsch proved that the Nottingham group over a finite field is verballyelliptic. We prove a similar result for fields of zero characteristic. We also provethat the Virasoro Lie algebra and some its subalgebras are polynomially elliptic

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KW - Lower Central Series

KW - Graded Lie algebra

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KW - Virasoro Algebra

KW - Witt Algebra

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VL - 574

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Verbal width in the Nottingham group and related Lie algebras

Abstract

Bibliographical note

Keywords

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