In this paper, we give a complete classification of eight dimensional nilpotent Lie algebras with four-dimensional center by using the method of Skjelbred and Sund.
In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solva...In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.展开更多
Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent...Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.展开更多
The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by...The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals.展开更多
In this note we consider 2-step nilpotent Lie algebras and give a criterion for the rigidity of this class in the variety N2n of 2-step nilpotent Lie algebras of dimension n. We apply this criterion to prove that ever...In this note we consider 2-step nilpotent Lie algebras and give a criterion for the rigidity of this class in the variety N2n of 2-step nilpotent Lie algebras of dimension n. We apply this criterion to prove that every rigid Lie algebra in N2n is indecomposable, except for η3 C and η3 η3.展开更多
THE theory of nilpotent Lie algebra is very important in the theory of finite-dimensional Lie al-gebras. Because of its extraordinary complexity, one usually studies various classes of specialnilpotent Lie algebras. I...THE theory of nilpotent Lie algebra is very important in the theory of finite-dimensional Lie al-gebras. Because of its extraordinary complexity, one usually studies various classes of specialnilpotent Lie algebras. In the study of complete Lie algebras, a class of special nilpotent Lie al-gebras (called completable nilpotent Lie algebras) was discovered. In this letter, we will展开更多
The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triang...The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.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
In this paper,we prove that the electrical Lie algebra e D_(5)is isomorphic to the semidirect product of sp_(4)and a 2-step nilpotent Lie algebra.Furthermore,we classify the irreducible highest weight modules for e D_...In this paper,we prove that the electrical Lie algebra e D_(5)is isomorphic to the semidirect product of sp_(4)and a 2-step nilpotent Lie algebra.Furthermore,we classify the irreducible highest weight modules for e D_(5).展开更多
Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such ...Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.展开更多
In this paper,based on Kac-Moody algebra,the isomorphic realization of nondegenerate solvable Lie algebras of maximal rank is given,which in turn revels the closed connections between nondegenerate solvable Lie algebr...In this paper,based on Kac-Moody algebra,the isomorphic realization of nondegenerate solvable Lie algebras of maximal rank is given,which in turn revels the closed connections between nondegenerate solvable Lie algebras and Kac-Moody algebras,resulting in some new worthy topics in this area.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.J1103110)
文摘In this paper, we give a complete classification of eight dimensional nilpotent Lie algebras with four-dimensional center by using the method of Skjelbred and Sund.
文摘In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.
文摘Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.
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.
基金Project supported by the the National Natural Science Foundation of China (No. 19971044) the Doctoral Program Foundation of the Ministry of Education of China (No. 97005511).
文摘The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals.
文摘In this note we consider 2-step nilpotent Lie algebras and give a criterion for the rigidity of this class in the variety N2n of 2-step nilpotent Lie algebras of dimension n. We apply this criterion to prove that every rigid Lie algebra in N2n is indecomposable, except for η3 C and η3 η3.
文摘THE theory of nilpotent Lie algebra is very important in the theory of finite-dimensional Lie al-gebras. Because of its extraordinary complexity, one usually studies various classes of specialnilpotent Lie algebras. In the study of complete Lie algebras, a class of special nilpotent Lie al-gebras (called completable nilpotent Lie algebras) was discovered. In this letter, we will
文摘The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.
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 the Fundamental Research Funds for the Central Universities(Grant No.2232021G-13).
文摘In this paper,we prove that the electrical Lie algebra e D_(5)is isomorphic to the semidirect product of sp_(4)and a 2-step nilpotent Lie algebra.Furthermore,we classify the irreducible highest weight modules for e D_(5).
基金Project supported by the National Natural Science Foundation of Chin
文摘Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.
基金supported by National Natural Science Foundation of China(Grant No.11071147)
文摘In this paper,based on Kac-Moody algebra,the isomorphic realization of nondegenerate solvable Lie algebras of maximal rank is given,which in turn revels the closed connections between nondegenerate solvable Lie algebras and Kac-Moody algebras,resulting in some new worthy topics in this area.
