论文标题
抗社会代数
Anti-associative algebras
论文作者
论文摘要
抗社会代数是一种非缔合代数，其乘法满足身份A（BC）+（AB）C = 0。这样的代数是nilpotent。我们描述了具有有限数量的发电机的自由反缔约代数。通过极化过程（例如Jacobi-Jordan代数，或通过变形量化获得）获得的其他类型的非缔合代数与该类别的代数相关。在Markl-Remms工作之后，我们描述了与这些代数类别相关的作战，尤其是与变形有关的共同体学络合物。
An anti-associative algebra is a nonassociative algebra whose multiplication satisfies the identity a(bc)+(ab)c=0. Such algebras are nilpotent. We describe the free anti-associative algebras with a finite number of generators. Other types of nonassociative algebras, obtained either by the process of polarization, such as Jacobi-Jordan algebras, or obtained by deformation quantization, are associated with this class of algebras. Following Markl-Remms work, we describe the operads associated with these algebra classes and in particular the cohomology complexes in relation to deformations.
