In our earlier paper,we generalize the one-parameter(c)family of inhomogeneous firstorder differential operator representations of the orthogonal Lie algebras arising from conformal transformations to those of orthosy...In our earlier paper,we generalize the one-parameter(c)family of inhomogeneous firstorder differential operator representations of the orthogonal Lie algebras arising from conformal transformations to those of orthosymplectic Lie super algebras,and determine the irreducible condition.This paper deals with the cases when the irreducible condition fails.We prove that if n-m-1>0 and c is an integer satisfying 1≤c≤n-m-1,the representation of osp(2n+2|2m)has a composition series of length 2,and when n-m-1≥0 and c∈-N,the representation of osp(2n+2|2m)has a composition series of length 3,where N is the set of nonnegative integers.Moreover,we show that if c∈(max{n-m,0}-1/2-N)∪(-N),the representation of osp(2n+3|2m)has a composition series of length 2.In particular,we obtain an explicit presentation of the irreducible module with highest weight lλ2-λ1,where l is any positive integer and it is not a generalized Verma module.展开更多
We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm 12n（R,-） that is coordinatized by an arbitrary unital associative superalgebra （R,-） with superinvol...We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm 12n（R,-） that is coordinatized by an arbitrary unital associative superalgebra （R,-） with superinvolution. As a result, an identification between the second homology group of the Lie superalgebra ospm｜2n （R,-） and the first skew-dihedral homology group of the associative superalgebra （R,-） with superin-volution is created for positive integers m and n with （m, n）≠ （1, 1） and （m, n）≠（2, 1）. The second homology groups of the Lie superalgebras ospm1｜2（R,-） and ospm｜2n （R,-） are also characterized explicitly.展开更多
基金Supported by National Key R&D Program of China(Grant No.2020YFA0712600)。
文摘In our earlier paper,we generalize the one-parameter(c)family of inhomogeneous firstorder differential operator representations of the orthogonal Lie algebras arising from conformal transformations to those of orthosymplectic Lie super algebras,and determine the irreducible condition.This paper deals with the cases when the irreducible condition fails.We prove that if n-m-1>0 and c is an integer satisfying 1≤c≤n-m-1,the representation of osp(2n+2|2m)has a composition series of length 2,and when n-m-1≥0 and c∈-N,the representation of osp(2n+2|2m)has a composition series of length 3,where N is the set of nonnegative integers.Moreover,we show that if c∈(max{n-m,0}-1/2-N)∪(-N),the representation of osp(2n+3|2m)has a composition series of length 2.In particular,we obtain an explicit presentation of the irreducible module with highest weight lλ2-λ1,where l is any positive integer and it is not a generalized Verma module.
基金supported by National Natural Science Foundation of China (Grant No. 11501213)the China Postdoctoral Science Foundation (Grant No. 2015M570705)+2 种基金the Fundamental Research Funds for the Central Universities (Grant No. 2015ZM085)the China Postdoctoral Science Foundation (Grant No. 2015M571928)the Fundamental Research Funds for the Central Universities
文摘We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm 12n（R,-） that is coordinatized by an arbitrary unital associative superalgebra （R,-） with superinvolution. As a result, an identification between the second homology group of the Lie superalgebra ospm｜2n （R,-） and the first skew-dihedral homology group of the associative superalgebra （R,-） with superin-volution is created for positive integers m and n with （m, n）≠ （1, 1） and （m, n）≠（2, 1）. The second homology groups of the Lie superalgebras ospm1｜2（R,-） and ospm｜2n （R,-） are also characterized explicitly.
