Derivations of Direct Limits of Lie Superalgebras |
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| Authors: | Malihe Yousofzadeh |
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| Institution: | 1. Department of Mathematics, University of Isfahan, Isfahan, Iran and School of Mathematics, Institute for Research in Fundamental Sciences, Tehran, Iranma.yousofzadeh@sci.ui.ac.ir ma.yousofzadeh@ipm.ir |
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| 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. |
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| Keywords: | Derivation Direct limit Inverse limit |
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