Gelfand-Kirillov dimension of brace algebras

Yu Li; Qiuhui Moa; Wenchao Zhang; Xiangui Zhao

doi:10.1080/00927872.2025.2469806

Gelfand-Kirillov dimension of brace algebras

Yu Li, Qiuhui Moa, Wenchao Zhang, Xiangui Zhao

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

Abstract

Over a field of characteristic zero, we prove that there exists a two-generated brace algebra of Gelfand-Kirillov dimension r for each real number (Formula presented.), that the Gelfand-Kirillov dimension of the universal enveloping brace algebra of a finite dimensional (left) pre-Lie algebra is either zero or infinity, and that the basic rank of the variety of brace algebras is 1.

Original language	English
Journal	Communications in Algebra
DOIs	https://doi.org/10.1080/00927872.2025.2469806
State	Accepted/In press - 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2025 Taylor & Francis Group, LLC.

Keywords

Gelfand-Kirillov dimension
Gröbner-Shirshov basis
basic rank
brace algebra

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10.1080/00927872.2025.2469806

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AU - Zhao, Xiangui

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N2 - Over a field of characteristic zero, we prove that there exists a two-generated brace algebra of Gelfand-Kirillov dimension r for each real number (Formula presented.), that the Gelfand-Kirillov dimension of the universal enveloping brace algebra of a finite dimensional (left) pre-Lie algebra is either zero or infinity, and that the basic rank of the variety of brace algebras is 1.

AB - Over a field of characteristic zero, we prove that there exists a two-generated brace algebra of Gelfand-Kirillov dimension r for each real number (Formula presented.), that the Gelfand-Kirillov dimension of the universal enveloping brace algebra of a finite dimensional (left) pre-Lie algebra is either zero or infinity, and that the basic rank of the variety of brace algebras is 1.

KW - Gelfand-Kirillov dimension

KW - Gröbner-Shirshov basis

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Gelfand-Kirillov dimension of brace algebras

Abstract

Bibliographical note

Keywords

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