A Class Of Lie Superalgebras Of ε-type

The present thesis is devoted to studying the structures and property a class of finite-dimensional modular Lie superalgebras of ε-type. Firstly, we give the definition of the modular Lie superalgebras ε-type and determine their simplicity. Then we determine the generators sets. By employed the generators sets, we determine the homogeneous su-perderivations of modular Lie superalgebras of ε. Furthermore, we determine completely the superderivation algebras of ε. Finally, we study the associative forms and Killing forms of these Lie superalgebras and find the conditions for the restrictability of these Lie superalgebras.