论文标题
Rota-Baxter操作员的频谱
Spectrum of Rota-Baxter operators
论文作者
论文摘要
我们证明，在特征零字段上的Unital代数（不一定是关联的）代数上，每个Rota-Baxter的重量$λ$的频谱是$ \ {0，-λ\} $的子集。对于有限的UNITAL代数，同一陈述显示在没有限制地面场的特征的情况下持有。基于这些结果，我们定义了rota-baxter $λ$ - index $ \ mathrm {rb}_λ（a）代数$ a $的$，是所有重量$λ$ a $ a $ a $ a $ a $的最小rota-baxter运算符的最小rota-baxter运算符。我们计算矩阵代数$ m_n（f）$，$ \ mathrm {char} \，f = 0 $：显示出$ \ mathrm {rb}_λ（m_n（f））= 2n-1 $。
We prove that the spectrum of every Rota-Baxter operator of weight $λ$ on a unital algebraic (not necessarily associative) algebra over a field of characteristic zero is a subset of $\{0,-λ\}$. For a finite-dimensional unital algebra the same statement is shown to hold without a restriction on the characteristic of the ground field. Based on these results, we define the Rota-Baxter $λ$-index $\mathrm{rb}_λ(A)$ of an algebra $A$ as the infimum of the degrees of minimal polynomials of all Rota-Baxter operators of weight $λ$ on $A$. We calculate the Rota-Baxter $λ$-index for the matrix algebra $M_n(F)$, $\mathrm{char}\,F = 0$: it is shown that $\mathrm{rb}_λ(M_n(F)) = 2n-1$.
