In this paper,we study irreducible non-weight modules over the mirror Heisenberg-Virasoro algebra D,including Whittaker modules,U(Cd_(0))-free modules and their tensor products.More precisely,we give the necessary and...In this paper,we study irreducible non-weight modules over the mirror Heisenberg-Virasoro algebra D,including Whittaker modules,U(Cd_(0))-free modules and their tensor products.More precisely,we give the necessary and sufficient conditions for the Whittaker modules to be irreducible.We determine all the D-module structures on U(Cd_(0)),and find the necessary and sufficient conditions for these modules to be irreducible.At last,we determine the necessary and sufficient conditions for the tensor products of Whittaker modules and U(Cd_(0))-free modules to be irreducible,and obtain that any two such tensor products are isomorphic if and only if the corresponding Whittaker modules and U(Cd_(0))-free modules are isomorphic.These lead to many new irreducible non-weight modules over D.展开更多
In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and th...In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.展开更多
基金supported by China Scholarship Council(Grant No.201906340096)National Natural Science Foundation of China(Grant Nos.11771410 and 11931009)+2 种基金supported by National Natural Science Foundation of China(Grant No.11801066)supported by National Natural Science Foundation of China(Grant No.11871190)Natural Sciences and Engineering Research Council of Canada(Grant No.311907-2020).
文摘In this paper,we study irreducible non-weight modules over the mirror Heisenberg-Virasoro algebra D,including Whittaker modules,U(Cd_(0))-free modules and their tensor products.More precisely,we give the necessary and sufficient conditions for the Whittaker modules to be irreducible.We determine all the D-module structures on U(Cd_(0)),and find the necessary and sufficient conditions for these modules to be irreducible.At last,we determine the necessary and sufficient conditions for the tensor products of Whittaker modules and U(Cd_(0))-free modules to be irreducible,and obtain that any two such tensor products are isomorphic if and only if the corresponding Whittaker modules and U(Cd_(0))-free modules are isomorphic.These lead to many new irreducible non-weight modules over D.
基金Supported by National Natural Science Foundation of China(Grant Nos.11431010,11371278 and 11271284)Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)
文摘In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.
