Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all doubl...Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all double derivations is a subalgebra of the general linear Lie superalgebra gl（9） and the inner derivation algebra ad（9） is an ideal of 7）（9）. We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad（9） in 7P（9） is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der（9） are exactly the derivations of Der（9）.展开更多
In this paper we discuss about the semiprimitivity and the semiprimality of partial smash products. Let H be a semisimple Hopf algebra over a field k and let A be a left partial H-module algebra. We study the H-prime ...In this paper we discuss about the semiprimitivity and the semiprimality of partial smash products. Let H be a semisimple Hopf algebra over a field k and let A be a left partial H-module algebra. We study the H-prime and the H-Jacobson radicals of A and their relations with the prime and the Jacobson radicals of A#H, respectively. In particular, we prove that if A is H-semiprimitive, then A^fH is semiprimitive provided that all irreducible representations of A are finite-dimensional, or A is an affine PI-algebra over k and k is a perfect field, or A is locally finite. Moreover, we prove that A=#=H is semiprime provided that A is an H-semiprime PI-algebra, generalizing to the setting of partial actions the known results for global actions of Hopf algebras.展开更多
文摘Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all double derivations is a subalgebra of the general linear Lie superalgebra gl（9） and the inner derivation algebra ad（9） is an ideal of 7）（9）. We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad（9） in 7P（9） is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der（9） are exactly the derivations of Der（9）.
文摘In this paper we discuss about the semiprimitivity and the semiprimality of partial smash products. Let H be a semisimple Hopf algebra over a field k and let A be a left partial H-module algebra. We study the H-prime and the H-Jacobson radicals of A and their relations with the prime and the Jacobson radicals of A#H, respectively. In particular, we prove that if A is H-semiprimitive, then A^fH is semiprimitive provided that all irreducible representations of A are finite-dimensional, or A is an affine PI-algebra over k and k is a perfect field, or A is locally finite. Moreover, we prove that A=#=H is semiprime provided that A is an H-semiprime PI-algebra, generalizing to the setting of partial actions the known results for global actions of Hopf algebras.
