论文标题
在谎言上superalgebra $ \ mathfrak {gl}（m | n）$重量系统
On the Lie superalgebra $\mathfrak{gl}(m|n)$ weight system
论文作者
论文摘要
对于有限类型的结，可以关联一个重量系统，这是满足所谓$ 4 $ term Relative的和弦图的功能。在相反的方向上，每个重量系统决定有限的结。特别是，重量系统可以与任何Metrized Lie代数相关联，任何Metrized lie superalgebra。但是，这些权重系统的计算很复杂。在本作者的最新论文中，定义了$ \ mathfrak {gl}（n）$ - 权重系统到任意排列的扩展，这允许人们开发一个复发关系，以有效地计算其值。此外，结果被证明是通用的，对$ n $的所有值有效，因此可以定义一个统一的$ \ mathfrak {gl} $ - 权重系统在无限的许多变量中占多项式中的值，$ c_0 = n，c_1，c_1，c_2，c_2，c_2，\ dots $。在本文中，我们将此构造扩展到与Lie Superalgebra $ \ Mathfrak {Gl}（M | N）$相关的重量系统。然后，我们证明了$ \ mathfrak {gl}（m | n）$ - 权重系统等效于$ \ mathfrak {gl} $ - 一个，一个，在替换下$ c_0 = m-n $。
To a finite type knot invariant, a weight system can be associated, which is a function on chord diagrams satisfying so-called $4$-term relations. In the opposite direction, each weight system determines a finite type knot invariant. In particular, a weight system can be associated to any metrized Lie algebra, and any metrized Lie superalgebra. However, computation of these weight systems is complicated. In the recent paper by the present author, an extension of the $\mathfrak{gl}(N)$-weight system to arbitrary permutations is defined, which allows one to develop a recurrence relation for an efficient computation of its values. In addition, the result proves to be universal, valid for all values of $N$ and allowing thus to define a unifying $\mathfrak{gl}$-weight system taking values in the ring of polynomials in infinitely many variables $C_0=N,C_1,C_2,\dots$. In the present paper, we extend this construction to the weight system associated to the Lie superalgebra $\mathfrak{gl}(m|n)$. Then we prove that the $\mathfrak{gl}(m|n)$-weight system is equivalent to the $\mathfrak{gl}$-one, under the substitution $C_0=m-n$.
