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I was reading Supersymmetry in Quantum Mechanics and got stuck in the various mathematical terminology like "Graded-Lie Algebra", "Super Algebra". Is there any good lecture notes concerning these topics, explaining the basic mathematics needed to understand supersymmetry. I know basic analysis, topology, and first course in group theory, but never encountered ring theory, modules etc.

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I would recommend the book: Introduction to superanalysis - edited by A.A. Kirillov. This book contains collected and edited published and unpublished manuscripts by F.A. Berezin who was one of the founding fathers of the subject. The book is at an introductory level, designated for newcomers to the field. Although, the matrial was written in the 70s of the last century, I think that it is still suited to most physics applications

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Introduction to Supersymmetry by Harald Muller-Kirsten and Armin Wiedemann has a nice section on Graded Lie Algebra, and many other mathematical aspects of SUSY, with lots of detailed exercises.

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Related question 35532. I suggest you, that you consult these references: wiki, preprint, and book.

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    $\begingroup$ Good refs, but at the risk of sounding petty I do wish people would link to ArXiv abstract pages instead of the PDF, which may be a temp file and/or become out of date if new versions of the paper are released! (ArXiv link fixed ;-) ) $\endgroup$ – John R Ramsden Dec 8 '12 at 7:35

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