发表机构
Indian Institute of Technology, Kharagpur（印度理工学院卡拉格普尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入统一结合共形代数与 Diassociative 代数的 Diassociative 共形代数，建立其与形式分布 Diassociative 代数的范畴等价，定义其上同调并证明 Gerstenhaber 代数结构，用于研究形变与扩张，并揭示平均算子与其的关联。
AI 中文摘要
本文引入了 Diassociative 共形代数，它统一了结合共形代数与 Diassociative 代数。我们证明了 Diassociative 共形代数的范畴等价于形式分布 Diassociative 代数的等价类范畴。通过利用其 Maurer-Cartan 刻画，我们定义了 Diassociative 共形代数的上同调，并证明其具有 Gerstenhaber 代数结构。我们的上同调可用于研究该结构的形变与扩张。最后，我们在结合共形代数上定义了平均算子，并发现了它们与 Diassociative 共形代数的密切联系。
英文摘要
In this paper, we introduce diassociative conformal algebras that unify both associative conformal algebras and diassociative algebras. We show that the category of diassociative conformal algebras is equivalent to the category of equivalence classes of formal distribution diassociative algebras. By employing its Maurer-Cartan characterization, we then define the cohomology of a diassociative conformal algebra and show that it carries a Gerstenhaber algebra structure. Our cohomology can be used to study deformations and extensions of the structure. Finally, we define averaging operators on associative conformal algebras and find their close relations with diassociative conformal algebras.
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