张量空间上的符号随机到顶算子（草稿）
The signed random-to-top operator on tensor space (draft)
摘要：
给定一个交换环k上的自由模L，研究T（L）的张量代数上的两个k-线性算子：其中一个发送纯张量u_1（X）u_2（X）. (X)u_k等于所有张量u_i（X）u_1（X）u_2（X）. (X)（skip u_i）（X）. (X)英国。另一个是类似的，但总和被替换为交替总和。这些运算符可以被视为组合数学中“随机到顶部洗牌”的代数类似物。我们描述了第二个算子的核（我们称之为黑体-t），它是T（L）的一个容易描述的李子超代数。我们还描述了第一个算子的核（用黑体字表示为t '），当加群k是挠自由的（描述类似于t的核），也当k是有限域上的代数时（在这种情况下，由于p次幂的存在，描述稍微复杂）。
英文摘要：
Given a free module L over a commutative ring k, we study two k-linear operators on the tensor algebra of T(L): One of them sends a pure tensor u_1 (X) u_2 (X) ... (X) u_k to the sum of all tensors u_i (X) u_1 (X) u_2 (X) ... (X) (skip u_i) (X) ... (X) u_k. The other is similar, but the sum is replaced by an alternating sum. These operators can be regarded as algebraic analogues of the "random-to-top shuffle" from combinatorics. We describe the kernel of the second operator (which we call boldface-t); it is a certain easily described Lie subsuperalgebra of T(L). We also describe the kernel of the first operator (which is denoted boldface-t') when the additive group k is torsionfree (the description is analogous to that of the kernel of t) and also when k is an algebra over a finite field (in this case, the description is slightly complicated by the presence of p-th powers).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
