The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvab...The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.展开更多
The finite-dimensional indecomposable solvable Lie algebras s with Q_(2n+1) as their nilradical are studied and classified and their Casimir invariants are calculated. It turns out that the dimension of s is at most d...The finite-dimensional indecomposable solvable Lie algebras s with Q_(2n+1) as their nilradical are studied and classified and their Casimir invariants are calculated. It turns out that the dimension of s is at most dim Q_(2n+1)+2.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
In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last p...In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（11071187） Supported by the Natural Science Foundation of Henan Province（13A110785）
文摘The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.
基金Supported by the National Natural Science Foundation of China(11071187)Supported by the Basic and Advanced Technology Research Project of Henan Province(142300410449)Supported by the Natural Science Foundation of Education Department of Henan Province(16A110035)
文摘The finite-dimensional indecomposable solvable Lie algebras s with Q_(2n+1) as their nilradical are studied and classified and their Casimir invariants are calculated. It turns out that the dimension of s is at most dim Q_(2n+1)+2.
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In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.
