On the modular Lie superalgebra Ω

A class of finite-dimensional simple modular Lie superalgebra Omega was constructed and its derivation superalgebra was determined in Zhang and Zhang (2009) [24]. The purpose of the present paper is to continue the investigation of finite-dimensional modular Lie superalgebra Omega. A nonnatural filtration of finite-dimensional modular Lie superalgebra Omega over a field of positive characteristic is determined. It is proved that the nonnatural filtration of Omega is invariant under the automorphism group of Omega. Moreover, we obtain the sufficient and necessary conditions of Omega(r, m, q, (s) under bar, H) congruent to Omega(r', m', q', (s) under bar', H'), i.e., we classified the Lie superalgebra of Omega type. (C) 2010 Elsevier B.V. All rights reserved.