We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(...We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(A) = A(?)D(A, M) is nilpotent in L(M).展开更多
We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in som...We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in some cases. These results could be used to associate geometric objects (loop spaces) to low dimensional Leibniz algebras.展开更多
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
In this paper, we mainly concerned about the nilpotence of Lie triple algebras.We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triplealgebra is nilpotent, then its standard enve...In this paper, we mainly concerned about the nilpotence of Lie triple algebras.We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triplealgebra is nilpotent, then its standard enveloping Lie algebra is nilpotent.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
In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type Ⅱ classical graded Lie algebras.
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
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
文摘We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M) = M(?)D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal I(A) = A(?)D(A, M) is nilpotent in L(M).
文摘We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in some cases. These results could be used to associate geometric objects (loop spaces) to low dimensional Leibniz algebras.
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
基金Supported by NKBRPC(2004CB31800)Supported by NNSFC(10375087)
文摘In this paper, we mainly concerned about the nilpotence of Lie triple algebras.We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triplealgebra is nilpotent, then its standard enveloping Lie algebra is nilpotent.
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 Australian Research Council(Grant No.DP150103525)。
文摘In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type Ⅱ classical graded Lie 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.
