论文标题
非缔约代数的变形量化
Deformation quantization of nonassociative algebras
论文作者
论文摘要
我们研究了某些类别的非社交代数的形式变形，包括k [σ3] - 缔合代数，li含量可加入的代数和抗社会代数的代数。在类似于泊松代数的过程中，我们为每种类型的代数（a，μ），代数（a，μ，ψ）确定的相关案例，使得形式变形（a [[t]，μt）是（a，μ，ψ）的量化变形。极化/去极化的过程与每个非社交代数相关，几个代数分别是换向且偏斜的，并与从形式变形获得的代数相关。与雅各比 - 约旦代数有联系，开发了反社会案例
We investigate formal deformations of certain classes of nonassociative algebras including classes of K[Σ3]-associative algebras, Lie-admissible algebras and anti-associative algebras. In a process which is similar to Poisson algebra for the associative case we identify for each type of algebra (A, μ), an algebra (A, μ, ψ) such that the formal deformation (A[[t]], μt) is the quantization deformation of (A, μ, ψ). The process of polarization/depolarization associate to each nonassociative algebra a couple of algebras which products are respectively commutative and skew-symmetric and is linked with the algebra obtained from the formal deformation. The anti-associative case is developed with a link with the Jacobi-Jordan algebras
