I am currently working with irreducible $k[G]$-modules in MAGMA for finite fields $k$ and finite groups $G$. To construct these modules, I am using the commands IrreducibleModules(G,k) This results in MAGMA recognising the modules as being of type $ModGrp$. However, I wish to perform calculations such as finding the projective cover of such a module, for which MAGMA can only perform such calculations on modules over algebras (i.e. of type $ModAlg$). Is there an easy way to coerce MAGMA into treating modules of type $ModGrp$ as being of type $ModAlg$?
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MAGMA is perfectly capable of calculating the projective cover of a member of IrreducibleModules(G,k), via the ProjectiveCover() function. You can also just call ProjectiveIndecomposables(G,k). Perhaps you are running an old version of MAGMA? Version 2.18-3 is certainly capable of this functionality.
(This would have been a comment rather than an answer if reputation allowed).
answered Apr 18, 2012 at 14:19
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$\begingroup$ Thanks for the comment. I have tried using these commands, but just get the error messages: Runtime error in 'ProjectiveCover': Bad argument types Argument types given: ModGrp. Perhaps it is as you suggested that the version of MAGMA that I am using is too old (it is V2.15-15) $\endgroup$ Apr 18, 2012 at 14:47
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1$\begingroup$ I believe the projective modules functionality was introduced in V2.17, so you will need to update. $\endgroup$ Apr 18, 2012 at 15:20
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$\begingroup$ @AlistariLitterick Thanks for clarifying that. $\endgroup$ Apr 18, 2012 at 15:22