二次Hom-Novikov超代数

吉林大学学报(理学版) ›› 2020, Vol. 58 ›› Issue (3): 545-549.

二次Hom-Novikov超代数

孙冰¹, 周鑫^2,3

1. 长春师范大学数学学院, 长春 130032; 2. 伊犁师范大学数学与统计学院, 新疆伊宁 835000;3. 东北师范大学数学与统计学院, 长春 130024

收稿日期:2019-08-07 出版日期:2020-05-26 发布日期:2020-05-20
通讯作者: 孙冰 E-mail:sunb427@nenu.edu.cn

Quadratic Hom-Novikov Superalgebras

SUN Bing¹, ZHOU Xin^2,3

1. School of Mathematics, Changchun Normal University, Changchun 130032, China;2. School of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China;3. School of Mathematical and Statistics, Northeast Normal University, Changchun 130024, China

Received:2019-08-07 Online:2020-05-26 Published:2020-05-20
Contact: SUN Bing E-mail:sunb427@nenu.edu.cn

摘要/Abstract

摘要： 将二次Novikov超代数通过一个扭曲映射推广到二次Hom-Novikov超代数. 当Hom-Novikov超代数中扭曲映射为自同构或对合时, 给出二次Hom-Novikov超代数与二次Novikov超代数之间的关系, 建立二次Hom-Novikov超代数与二次Hom-李超代数之间的联系, 并证明二次Hom-Novikov超代数是Hom结合代数, 且Hom-Novikov超代数的邻接Hom-李超代数是2-步幂零的.

关键词: Novikov超代数, Hom-Novikov超代数, 二次Hom-Novikov超代数

Abstract: We extended the quadratic Novikov superalgebras to quadratic HomNovikov superalgebras by a twisting map.
When the twisting map in HomNovikov superalgebra was an automorphism or an involution, we gave the relationships between quadratic Hom-Novikov superalgebras and quadratic Novikov superalgebras, established the relations between quadratic Hom-Novikov superalgebras and quadratic Hom Lie superalgebras, proved that quadratic Hom-Novikov superalgebras were Hom associative algebras, and the adjacent Hom Lie superalgebras of quadratic Hom-Novikov superalgebras were 2step nilpotent.

Key words: Novikov superalgebra, HomNovikov superalgebra, quadratic HomNovikov superalgebra

中图分类号:

O159

孙冰, 周鑫. 二次Hom-Novikov超代数[J]. 吉林大学学报(理学版), 2020, 58(3): 545-549.

SUN Bing, ZHOU Xin. Quadratic Hom-Novikov Superalgebras[J]. Journal of Jilin University Science Edition, 2020, 58(3): 545-549.