Derivations of Direct Limits of Lie Superalgebras

Abstract

We describe the derivations of a direct limit 𝔏 of Lie superalgebras 𝔏i (i ∈ I) in an 𝔏-module 𝔲 as the inverse limit of the derivations of 𝔏i's in 𝔲. Using this, in case the first cohomology group of each 𝔏i with coefficients in 𝔲 is zero, we describe the derivations of 𝔏 in 𝔲 as the inverse limit of 𝔲/𝔲𝔏i (i ∈ I). This then allows us to compute the derivations of direct limits of finite-dimensional basic classical simple Lie superalgebras. © 2016, Copyright © Taylor & Francis Group, LLC.