Lie-admissible structures on a class of Block Lie algebras ℬ(q)

Lamei Yuan; Yuhui Tan

doi:10.1080/00927872.2025.2520383

Lie-admissible structures on a class of Block Lie algebras ℬ(q)

Lamei Yuan^*
, Yuhui Tan

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

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

Abstract

The Block algebra (Formula presented.) referred to here is the complex Lie algebra with basis (Formula presented.) and subject to the commutation relations (Formula presented.) where q is a fixed complex number. In this paper, we describe all third-power associative multiplications (Formula presented.) on (Formula presented.) provided that (Formula presented.) for all (Formula presented.). We also obtain necessary and sufficient conditions for these multiplications to be flexible.

Original language	English
Pages (from-to)	139-148
Number of pages	10
Journal	Communications in Algebra
Volume	54
Issue number	1
DOIs	https://doi.org/10.1080/00927872.2025.2520383
State	Published - 2026
Externally published	Yes

Keywords

Block Lie algebra
Lie-admissible algebras
flexible
third-power associative

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10.1080/00927872.2025.2520383

Cite this

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abstract = "The Block algebra (Formula presented.) referred to here is the complex Lie algebra with basis (Formula presented.) and subject to the commutation relations (Formula presented.) where q is a fixed complex number. In this paper, we describe all third-power associative multiplications (Formula presented.) on (Formula presented.) provided that (Formula presented.) for all (Formula presented.). We also obtain necessary and sufficient conditions for these multiplications to be flexible.",

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AB - The Block algebra (Formula presented.) referred to here is the complex Lie algebra with basis (Formula presented.) and subject to the commutation relations (Formula presented.) where q is a fixed complex number. In this paper, we describe all third-power associative multiplications (Formula presented.) on (Formula presented.) provided that (Formula presented.) for all (Formula presented.). We also obtain necessary and sufficient conditions for these multiplications to be flexible.

KW - Block Lie algebra

KW - Lie-admissible algebras

KW - flexible

KW - third-power associative

UR - https://www.scopus.com/pages/publications/105009525932

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M3 - 文章

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JO - Communications in Algebra

JF - Communications in Algebra

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Lie-admissible structures on a class of Block Lie algebras ℬ(q)

Abstract

Keywords

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