A complete description of all the infinitesimal deformations of the Lie superalgebra Ln,m

作者：Khakimdjanov Yu; Navarro R M^*

来源：Journal of Geometry and Physics, 2010, 60(1): 131-141.

DOI：10.1016/j.geomphys.2009.09.002

• Lie algebras
• Lie superalgebras
• Cohomology
• Deformation
• Nilpotent
• Filiform

In this paper, we find the dimension and a method to obtain a basis of some infinitesimal deformations of the model Lie superalgebra L(n,m). These deformations lie in Hom(L(n) boolean AND V(1), V(1)) being L(n) and V(1) the even and odd parts of the Lie superalgebra L(n,m) respectively. As L(n) corresponds to the model filiform Lie algebra, then these deformations can also be identified with the space of the infinitesimal deformations of the filiform L(n)-module V(1). Combining with Bordemann et al. (2007)[2], Gomez et al. (2008) [3] and Khakimdjanov and Navarro [4] we therefore obtain a complete classification of all the infinitesimal deformations of the model Lie superalgebra L(n,m).

• 出版日期2010-1