论文标题
第三维数和约旦代数的复杂联想代数的退化
Degenerations of complex associative algebras of dimension three via Lie and Jordan algebras
论文作者
论文摘要
令$ \BoldSymbolλ_3（\ Mathbb C）\，（= \ Mathbb C^{27}）$是结构向量的空间，$ 3 $ -Dimensional代数超过$ \ Mathbb c $，被认为是$ G $ -MODULE，通过$ G $ -MODULE，通过$ G $ = { $ \boldsymbolλ_3（\ Mathbb C）$`通过更改基础'。我们确定代数子集内部的完整变性图片$ \ Mathcal a^s_3 $ of $ \boldsymbolλ_3（\ Mathbb c）$由联想代数结构组成的结构通过代数子集的相应信息组成和约旦代数结构。这是在某些$ g $ -Module内态$ ϕ_1 $，$ ϕ_2 $ $ \boldsymbolλ_3（\ Mathbb c）$的帮助下实现的，这些$ \boldsymbolλ_3（\ Mathbb c）$ sap $ \ mathcal a^s_3 $ to a^s_3 $ to $ \ Mathcal l_3 $ and $ \ Mathcal l_3 $ and $ \ MATHCAL J_3 $相差。
Let $\boldsymbolΛ_3(\mathbb C)\,(=\mathbb C^{27})$ be the space of structure vectors of $3$-dimensional algebras over $\mathbb C$ considered as a $G$-module via the action of $G={\rm GL}(3,\mathbb C)$ on $\boldsymbolΛ_3(\mathbb C)$ `by change of basis'. We determine the complete degeneration picture inside the algebraic subset $\mathcal A^s_3$ of $\boldsymbolΛ_3(\mathbb C)$ consisting of associative algebra structures via the corresponding information on the algebraic subsets $\mathcal L_3$ and $\mathcal J_3$ of $\boldsymbolΛ_3(\mathbb C)$ of Lie and Jordan algebra structures respectively. This is achieved with the help of certain $G$-module endomorphisms $ϕ_1$, $ϕ_2$ of $\boldsymbolΛ_3(\mathbb C)$ which map $\mathcal A^s_3$ onto algebraic subsets of $\mathcal L_3$ and $\mathcal J_3$ respectively.
