DUAL COALGEBRAS OF JACOBIAN n-LIE ALGEBRAS OVER POLYNOMIAL RINGS

被引：0

作者：

Zhelyabin, V. N. ^{[1
]}

Kolesnikov, P. S. ^{[1
]}

机构：

[1] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2023年 / 64卷 / 05期

关键词：

coalgebra; Poisson bracket; Filippov algebra; Jacobian; 512.554.7; CO-ALGEBRA; JORDAN; CONSTRUCTION;

D O I：

10.1134/S0037446623050087

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the structure of the dual Lie coalgebra for a Lie algebra of the symplectic Poisson bracket (Jacobian-type Poisson bracket) on the algebra of polynomials in evenly many variables. We show that if the base field has characteristic zero then the n-ary dual coalgebra for the Jacobian n-Lie algebra consists of the same linear functionals as the dual coalgebra for the commutative polynomial algebra.

引用

页码：1153 / 1166

页数：14

共 23 条

[1] NONASSOCIATIVE COALGEBRAS [J].