The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the h...The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.展开更多
We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and gener...We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for op（kl2n）. Furthermore, we discuss the harmonic representative elements of the Kostant＇s u-cohomology with trivial coefficients.展开更多
基金The Natural Science Foundation of Jiangsu Province(No.BK2012736)the Natural Science Foundation of Chuzhou University(No.2010kj006Z)
文摘The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.
基金supported by National Natural Science Foundation of China(Grant Nos.11101436 and 11101151)the Fundamental Research Funds for the Central Universities
文摘We show that the denominator identity for ortho-symplectic Lie superalgebras 0sp（kl2n） is equiva- lent to the Littlewood＇s formula. Such an equivalence also implies the relation between the trivial module and generalized Verma modules for op（kl2n）. Furthermore, we discuss the harmonic representative elements of the Kostant＇s u-cohomology with trivial coefficients.
