All complex 3-dimensional nilalgebras were described.As a corollary,all degenerations in the variety of complex 3-dimensional nilalgebras were obtained.
We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan ...We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan algebra of level one.Moreover,we discuss marginal algebras in associative,alternative,left alternative,non-commutative Jordan,Leibniz and anticommutative cases.展开更多
In this article,we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras,bicommutative algebras,and assosymmetric algebras.More precisely,we first study the properties of t...In this article,we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras,bicommutative algebras,and assosymmetric algebras.More precisely,we first study the properties of the lower central chains for Novikov algebras and bicommutative algebras.Then we show that for every Lie nilpotent Novikov algebra or Lie nilpotent bicommutative algebra A,the ideal of A generated by the set{ab−ba|a,b∈A}is nilpotent.Finally,we study properties of the lower central chains for assosymmetric algebras,study the products of commutator ideals of assosymmetric algebras and show that the products of commutator ideals have a similar property as that for associative algebras.展开更多
基金supported by FCT UIDB/MAT/00212/2020UIDP/MAT/00212/2020.
文摘All complex 3-dimensional nilalgebras were described.As a corollary,all degenerations in the variety of complex 3-dimensional nilalgebras were obtained.
基金supported by FAPESP(16/16445-0,18/15712-0),RFBR(18-31-00001)the President's Program Support of Young Russian Scientists(grant MK-2262.2019.1).
文摘We describe all degenerations of the variety ■3 of Jordan algebras of dimension three over C.In particular,we describe all irreducible components in ■3.For every n we define an n-dimensional rigid“marginal”Jordan algebra of level one.Moreover,we discuss marginal algebras in associative,alternative,left alternative,non-commutative Jordan,Leibniz and anticommutative cases.
基金supported by FCT(Grant No.UIDB/00212/2020)FCT(Grant No.UIDP/00212/2020)+5 种基金supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan(Grant No.AP14869221)by“Tayelsizdik urpaqtary”MISD RKpartially supported by the Simons Foundation Targeted Grant for the Institute of Mathematics–VAST(Grant No.558672)by the Vietnam Institute for Advanced Study in Mathematics(VIASM)supported by the NNSF of China(Grant No.12101248)by the China Postdoctoral Science Foundation(Grant No.2021M691099)。
文摘In this article,we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras,bicommutative algebras,and assosymmetric algebras.More precisely,we first study the properties of the lower central chains for Novikov algebras and bicommutative algebras.Then we show that for every Lie nilpotent Novikov algebra or Lie nilpotent bicommutative algebra A,the ideal of A generated by the set{ab−ba|a,b∈A}is nilpotent.Finally,we study properties of the lower central chains for assosymmetric algebras,study the products of commutator ideals of assosymmetric algebras and show that the products of commutator ideals have a similar property as that for associative algebras.
基金supported by FAPESP 2019/03655-4,CNPq 302980/2019-9,RFBR 20-01-00030,MTM2016-79661-P,AP08052405 of MES RK,FPU scholarship(Spain)FCT UIDB/00212/2020 and UIDP/00212/2020+1 种基金supported by the Austrian Science Foundation FWF,grant P 33811-N,by Agencia Estatal de Investigación(Spain),grant PID2020-115155GB-I00(European FEDER support included,UE)by Xunta de Galicia,grant ED431C 2019/10(European FEDER support included,UE).
文摘We give a classification of 5-and 6-dimensional complex one-generated nilpotent bicommutative algebras.
