论文标题
二次和符号反异想代化代数的双重构造
Double constructions of quadratic and sympletic antiassociative algebras
论文作者
论文摘要
这项工作介绍了$ q $ generalized的关联代数和$ q $ generalized dendriform代数的一些相关特征和属性，例如双模式，匹配对。我们为$ Q = -1 $的特殊情况构建反异态自共介式代数，并将其直接分解为另一个反异态共聚物代数的基础矢量空间的直接总和，以使它们俩都是亚位式的，因此自然对称性双线性形式是不变的或自然的抗抗抗物性比较比较的表格。前者称为二次反异想加代词代数的双重结构，后来是符号反异性共聚物代数的双重结构，该代数用抗denderrifom代数来解释。我们对二维抗异基位式代数进行了分类，并彻底提供了一些双重构造的二次和符号反异性养殖代数。
This work addresses some relevant characteristics and properties of $q$-generalized associative algebras and $q$-generalized dendriform algebras such as bimodules, matched pairs. We construct for the special case of $q=-1$ an antiassociative algebra with a decomposition into the direct sum of the underlying vector spaces of another antiassociative algebra and its dual such that both of them are subalgebras and the natural symmetric bilinear form is invariant or the natural antisymmetric bilinear form is sympletic. The former is called a double construction of quadratic antiassociative algebra and the later is a double construction of sympletic antiassociative algebra which is interpreted in terms of antidendrifom algebras. We classify the 2-dimensional antiassociative algebras and thoroughly give some double constructions of quadratic and sympletic antiassociative algebras.
