山西大学学报（自然科学版）2026，Vol.49Issue(1)：71-77,7.DOI:10.13451/j.sxu.ns.2024017
完备Witt李代数的1/2-导子及转置泊松结构
1/2-Derivations and Transposed Poisson Structures on the Completed Witt Lie Algebra
摘要
Abstract
The completed Witt Lie algebra (L) is a Lie algebra consisting of derivations of the algebra of formal series.We determine all 1/2-derivations of (L).We prove transposed Poisson structures of (L) are nontrivial,and the general form of multiplication of trans-posed Poisson structures of (L) is(∞∑i=-1xiLi)·(∞∑j=-1yjLj)=∞∑q=-1(∑i∑jxiyjaq-i-j)Lq,where a1,a2,…∈C.Similar results are also obtained for the generalized completed Witt Lie algebra.关键词
完备Witt李代数/广义完备Witt李代数/1/2-导子/转置泊松结构Key words
completed Witt Lie algebra/generalized completed Witt Lie algebra/1/2-derivation/transposed Poisson structure分类
数理科学引用本文复制引用
张雯婷,吴鹤楠..完备Witt李代数的1/2-导子及转置泊松结构[J].山西大学学报（自然科学版）,2026,49(1):71-77,7.基金项目
国家自然科学基金(11701345) （11701345）
