This paper deals with injective and projective right HomH-modules for a Hom-algebra H. In particular, Baer Criterion of injective Hom-module is obtained, and it is shown that Hom Mod H is an Abelian category. Next, th...This paper deals with injective and projective right HomH-modules for a Hom-algebra H. In particular, Baer Criterion of injective Hom-module is obtained, and it is shown that Hom Mod H is an Abelian category. Next, the authors define Hom-path algebras and construct Hom-path algebras of some quivers.展开更多
Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz ...Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili.展开更多
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
In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain ...In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11271119,11201314)the Natural Science Foundation of Beijing(No.1122002)
文摘This paper deals with injective and projective right HomH-modules for a Hom-algebra H. In particular, Baer Criterion of injective Hom-module is obtained, and it is shown that Hom Mod H is an Abelian category. Next, the authors define Hom-path algebras and construct Hom-path algebras of some quivers.
基金Supported by the NNSF of China(11426095)the Foundation of Henan Educational Committee(14B110003)+3 种基金the NSF of Henan Province(152300410086)the Research Fund of PhD(qd14151)the Chuzhou University Excellent Young Talents Fund Project(2013RC001)the NSF of Chuzhou University(2014PY08)
基金Supported by National Natural Science Foundation of China （Grant Nos. 10825101, 11047030） and Natural Science Foundation of He＇nan Provincial Education Department （Grant No. 2010Bl10003）
文摘Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili.
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（11047030, 11171055） Supported by the Grant from China Scholarship Counci1（2011841026）
文摘In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.
