The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a re...The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.展开更多
Using the quiver technique we construct a class of non-graded bi-Frobenius algebras. We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.
In this paper, it is proved that the global dimension of a Yetter-Drinfel’d Hopf algebra coincides with the projective dimension of its trivial module k.
In this paper,we first give a direct sum decomposition of Lie comodules,and then accord- ing to the Lie comodule theory,construct some(triangular)Lie bialgebras through Lie coalgebras.
基金This work was partially supported by the Program for New Century Excellent Talents in University (Grant No.04-0522) the National Natural Science Foundation of China (Grant No.10571153).
文摘The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.10501041,10271113,10601052)
文摘Using the quiver technique we construct a class of non-graded bi-Frobenius algebras. We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.
基金supported by National Natural Science Foundation of China (Grant No. 10726039)the Leading Academic Discipline Program and 211 Project for Shanghai University of Finance and Economics (the 3rd phase)
文摘In this paper, it is proved that the global dimension of a Yetter-Drinfel’d Hopf algebra coincides with the projective dimension of its trivial module k.
基金the Educational Ministry Key Foundation of China(Grant No.108154)the National Natural Science Foundation of China(Grant No.10571153)
文摘In this paper,we first give a direct sum decomposition of Lie comodules,and then accord- ing to the Lie comodule theory,construct some(triangular)Lie bialgebras through Lie coalgebras.
