论文标题
转移的泊松代数，诺维科夫 - 波森代数和3 lie代数
Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras
论文作者
论文摘要
我们通过交换两个二进制操作的作用在莱布尼兹统治中定义了泊松代数的统治中，介绍了泊松代数的双重概念。我们表明，转泊泊松代数因此定义不仅具有泊松代数的共同特性，包括张张量产品下的封闭和koszul自二性作为operad，而且承认了一大批身份。更重要的是，换泊泊森代数自然源自诺维科夫代数的换向器代数来产生诺维科夫 - 波森代数。因此，在有一个派生时，带有一对通勤派生的泊松代数的经典结构具有相似的转换泊松代数的结构。更广泛地说，转移的泊松代数还捕获了换向器的托管前泊松代数和其他两个泊松型代数时，也捕获了代数结构。此外，转移的泊松代数改善了〜[17]中的两个过程，这些过程从泊松代数中产生3个lie代数，具有较强的条件。当在一个过程中使用转移的泊松代数时，不再需要强度条件，并且由此产生的3-lie代数给出了转移的泊松3-lie代数。在另一个过程中，结果表明，产生的3-lie代数再次给出了转移的泊松3-lie代数。
We introduce a dual notion of the Poisson algebra by exchanging the roles of the two binary operations in the Leibniz rule defining the Poisson algebra. We show that the transposed Poisson algebra thus defined not only shares common properties of the Poisson algebra, including the closure under taking tensor products and the Koszul self-duality as an operad, but also admits a rich class of identities. More significantly, a transposed Poisson algebra naturally arises from a Novikov-Poisson algebra by taking the commutator Lie algebra of the Novikov algebra. Consequently, the classic construction of a Poisson algebra from a commutative associative algebra with a pair of commuting derivations has a similar construction of a transposed Poisson algebra when there is one derivation. More broadly, the transposed Poisson algebra also captures the algebraic structures when the commutator is taken in pre-Lie Poisson algebras and two other Poisson type algebras. Furthermore, the transposed Poisson algebra improves two processes in~[17] that produce 3-Lie algebras from Poisson algebras with a strongness condition. When transposed Poisson algebras are used in one process, the strongness condition is no longer needed and the resulting 3-Lie algebra gives a transposed Poisson 3-Lie algebra. In the other process, the resulting 3-Lie algebra is shown to again give a transposed Poisson 3-Lie algebra.
