完备Witt李代数的1/2-导子及转置泊松结构OA
1/2-Derivations and Transposed Poisson Structures on the Completed Witt Lie Algebra
完备Witt李代数(L)是由形式幂级数代数的导子构成的李代数.我们确定了(L)的所有1/2-导子,证明了(L)有非平凡的转置泊松结构,并且给出了(L)的转置泊松结构的乘法的一般形式为(∞∑i=-1xiLi)·(∞∑j=-1yjLj)=∞∑q=-1(∑i∑jxiyjaq-i-j)Lq,其中,a1,a2,…∈C.对广义的完备Witt 李代数也得到了类似的结果.
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.
张雯婷;吴鹤楠
山西大学 数学科学学院,山西 太原 030006山西大学 数学科学学院,山西 太原 030006
数理科学
完备Witt李代数广义完备Witt李代数1/2-导子转置泊松结构
completed Witt Lie algebrageneralized completed Witt Lie algebra1/2-derivationtransposed Poisson structure
《山西大学学报（自然科学版）》 2026 (1)
71-77,7
国家自然科学基金(11701345)
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