This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semi...This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semisimple Lie superalgebra and M is an irreducible faithful L module.展开更多
We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov.This generalization is not so restrictive but sufficient enough so that we are able to have a classification for this generalized P(N)-graded Lie su...We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov.This generalization is not so restrictive but sufficient enough so that we are able to have a classification for this generalized P(N)-graded Lie superalgebras.Our result is that the generalized P(N)-graded Lie superalgebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a super-involution.Moreover,L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial.This recovers Martinez-Zelmanov’s theorem for type P(N).We also obtain a generalization of Kac’s coordinatization via Tits-Kantor-Koecher construction.Actually,the motivation of this generalization comes from the Fermionic-Bosonic module construction.展开更多
文摘This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semisimple Lie superalgebra and M is an irreducible faithful L module.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11701340,11931009)and the NSERC of Canada.
文摘We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov.This generalization is not so restrictive but sufficient enough so that we are able to have a classification for this generalized P(N)-graded Lie superalgebras.Our result is that the generalized P(N)-graded Lie superalgebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a super-involution.Moreover,L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial.This recovers Martinez-Zelmanov’s theorem for type P(N).We also obtain a generalization of Kac’s coordinatization via Tits-Kantor-Koecher construction.Actually,the motivation of this generalization comes from the Fermionic-Bosonic module construction.
