2023
DOI: 10.1007/s13398-022-01385-4
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The algebraic and geometric classification of transposed Poisson algebras

Abstract: The algebraic and geometric classification of all complex 3-dimensional transposed Poisson algebras is obtained. Also we discuss special 3-dimensional transposed Poisson algebras.

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Cited by 14 publications
(11 citation statements)
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“…The variety of transposed Poisson algebras gives a subvariety in C 2n 3 . The geometric classification of complex 3-dimensional transposed Poisson algebras was given in [6]. Neretin, in his paper [65], considered n-dimensional associative, commutative, and Lie algebras, and gave the upper bound for the dimensions of their geometric varieties.…”
Section: Question 19 Are Transposed Poisson Brackets Embeddable Into ...mentioning
confidence: 99%
“…The variety of transposed Poisson algebras gives a subvariety in C 2n 3 . The geometric classification of complex 3-dimensional transposed Poisson algebras was given in [6]. Neretin, in his paper [65], considered n-dimensional associative, commutative, and Lie algebras, and gave the upper bound for the dimensions of their geometric varieties.…”
Section: Question 19 Are Transposed Poisson Brackets Embeddable Into ...mentioning
confidence: 99%
“…Moreover, the algebra L 2 is a perfect algebra (i.e., [L 2 , L 2 ] = L 2 ) and admits non-trivial 1 2 -derivations. The existence of algebras with this property gives a particular answer to [4,Questions 2 and 5].…”
Section: Transposed Poisson Structure On Perfect Lie Algebrasmentioning
confidence: 99%
“…Any complex finite-dimensional solvable Lie algebra was proved to admit a non-trivial transposed Poisson structure [21]. The algebraic and geometric classification of 3-dimensional transposed Poisson algebras was given in [4]. For the list of actual open questions on transposed Poisson algebras, see [5].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…It was proved that any complex finite-dimensional solvable Lie algebra admits a non-trivial transposed Poisson structure [23]. The algebraic and geometric classification of 3dimensional transposed Poisson algebras was given in [5]. For the list of current open questions on transposed Poisson algebras, see [6].…”
Section: Introductionmentioning
confidence: 99%