Left-symmetric conformal algebras and vertex algebras

Hong, Yanyong; Li, Fang

doi:10.1016/j.jpaa.2014.12.012

Cited by 19 publications

(18 citation statements)

References 40 publications

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“…Then the conclusion follows if we prove that ( 19), ( 9), ( 10) and ( 11) are mutually equivalent, (20) and ( 13) are equivalent. As an example, we give an explicit proof that (20) holds if and only if (13) holds. The other cases can be proved similarly.…”

Section: Double Constructions Of Frobenius Conformal Algebrasmentioning

confidence: 99%

“…They were studied widely on the structure theory ( [4,5,6,8,10,11,18,20,22,26,27,28,29,30,31,32]) as well as representation theory ( [7,21,23]). We would like to point that there are the "conformal analogues" for certain algebras besides Lie and associative algebras or the "conformal structures" of these algebras such as left-symmetric conformal algebras ( [13]) and Jordan conformal algebras ( [19]).…”

Section: Introductionmentioning

confidence: 99%

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On antisymmetric infinitesimal conformal bialgebras

Hong

Bai

2021

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In this paper, we construct a bialgebra theory for associative conformal algebras, namely antisymmetric infinitesimal conformal bialgebras. On the one hand, it is an attempt to give conformal structures for antisymmetric infinitesimal bialgebras. On the other hand, under certain conditions, such structures are equivalent to double constructions of Frobenius conformal algebras, which are associative conformal algebras that are decomposed into the direct sum of another associative conformal algebra and its conformal dual as C[∂]-modules such that both of them are subalgebras and the natural conformal bilinear form is invariant. The coboundary case leads to the introduction of associative conformal Yang-Baxter equation whose antisymmetric solutions give antisymmetric infinitesimal conformal bialgebras. Moreover, the construction of antisymmetric solutions of associative conformal Yang-Baxter equation is given from O-operators of associative conformal algebras as well as dendriform conformal algebras.

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Section: Double Constructions Of Frobenius Conformal Algebrasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On antisymmetric infinitesimal conformal bialgebras

Hong

Bai

2021

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“…Then Coeff(R) is a (Lie or left-symmetric) algebra (see [14]). Any compatible left-symmetric conformal algebra over V ir is of the following form (see Theorem 3.2 in [12]):…”

Section: Preliminariesmentioning

confidence: 99%

Classification of compatible left-symmetric conformal algebraic structures on the Lie conformal algebra W(a,b)

Liu¹,

Hong²,

Zhou³

et al. 2018

Communications in Algebra

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“…In this section, we recall some definitions, notations and results about conformal algebras. Most of the results in this section can be found in [16,15].…”

Section: Preliminaries On Conformal Algebrasmentioning

confidence: 99%

“…On the other hand, a vertex algebra is a "combination" of a Lie conformal algebra and another algebraic structure, namely a left-symmetric algebra, satisfying certain compatible conditions ( [4]). Moreover, for studying whether there exist compatible left-symmetric algebra structures on formal distribution Lie algebras, the definition of left-symmetric conformal algebra was introduced in [15], which can be used to construct vertex algebras.…”

Section: Introductionmentioning

confidence: 99%

Conformal classical Yang-Baxter equation, $S$-equation and $\mathcal{O}$-operators

Hong,

Bai

2018

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Conformal classical Yang-Baxter equation and S-equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras. In this paper, they are interpreted in terms of a kind of operators, namely, O-operators in the conformal sense. Explicitly, the skew-symmetric part of a conformal linear map T where T0 = T λ | λ=0 is an O-operator in the conformal sense is a skew-symmetric solution of conformal classical Yang-Baxter equation, whereas the symmetric part is a symmetric solution of conformal S-equation. One byproduct is that a finite left-symmetric conformal algebra which is a free C[∂]-module gives a natural O-operator and hence there is a construction of solutions of conformal classical Yang-Baxter equation and conformal S-equation from the former. Another byproduct is that the non-degenerate solutions of these two equations correspond to 2-cocycles of Lie conformal algebras and left-symmetric conformal algebras respectively. We also give a further study on a special class of O-operators called Rota-Baxter operators on Lie conformal algebras and some explicit examples are presented.

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Left-symmetric conformal algebras and vertex algebras

Cited by 19 publications

References 40 publications

On antisymmetric infinitesimal conformal bialgebras

On antisymmetric infinitesimal conformal bialgebras

Classification of compatible left-symmetric conformal algebraic structures on the Lie conformal algebra W(a,b)

Conformal classical Yang-Baxter equation, $S$-equation and $\mathcal{O}$-operators

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