南方科技大学知识苑(SUSTech KC): On Pre-Novikov Algebras and Derived Zinbiel Variety

题名	On Pre-Novikov Algebras and Derived Zinbiel Variety
作者	Kolesnikov, Pavel 1; Mashurov, Farukh 2; Sartayev, Bauyrzhan 3,4
通讯作者	Kolesnikov, Pavel
发表日期	2024
DOI	10.3842/SIGMA.2024.017
发表期刊	SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 影响因子和分区
ISSN	1815-0659
卷号	20
摘要	For a non-associative algebra A with a derivation d, its derived algebra A(d) is the same space equipped with new operations a > b=d(a)b, a < b=ad(b), a, b is an element of A. Given a variety Var of algebras, its derived variety is generated by all derived algebras A(d) for all A in Var and for all derivations d of A. The same terminology is applied to binary operads governing varieties of non-associative algebras. For example, the operad of Novikov algebras is the derived one for the operad of (associative) commutative algebras. We state a sufficient condition for every algebra from a derived variety to be embeddable into an appropriate differential algebra of the corresponding variety. We also find that for Var=Zinb, the variety of Zinbiel algebras, there exist algebras from the derived variety (which coincides with the class of pre-Novikov algebras) that cannot be embedded into a Zinbiel algebra with a derivation.
关键词	Novikov algebra derivation dendriform algebra Zinbiel algebra
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	其他
资助项目	Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan[AP14870282] ; Program of Fundamental Research RAS[FWNF-2022-0002]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics ; Physics, Mathematical
WOS记录号	WOS:001177272600001
出版者	NATL ACAD SCI UKRAINE, INST MATH
来源库	Web of Science
引用统计	被引频次[WOS]：1
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/788892
专题	南方科技大学
作者单位	1.Sobolev Inst Math, Novosibirsk, Russia 2.Southern Univ Sci & Technol, Shenzhen Int Ctr Math SICM, Shenzhen, Guangdong, Peoples R China 3.Narxoz Univ, Alma Ata, Kazakhstan 4.United Arab Emirates Univ, Al Ain, U Arab Emirates
推荐引用方式 GB/T 7714	Kolesnikov, Pavel,Mashurov, Farukh,Sartayev, Bauyrzhan. On Pre-Novikov Algebras and Derived Zinbiel Variety[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS,2024,20.
APA	Kolesnikov, Pavel,Mashurov, Farukh,&Sartayev, Bauyrzhan.(2024).On Pre-Novikov Algebras and Derived Zinbiel Variety.SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS,20.
MLA	Kolesnikov, Pavel,et al."On Pre-Novikov Algebras and Derived Zinbiel Variety".SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 20(2024).