Does anybody know good references to learn about Lie superalgebras? I started with Howe's "Remarks on classical invariant theory", which contains a study of osp(m,2n), and now I am reading Kac's '77 Advances paper. I wonder if there are other helpful sources. I am especially interested in getting a feel for the representation theory.
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6 Answers
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Have you seen the survey by Frappat-Sciarrino-Sorba, "Dictionary on Lie Superalgebras" listed here?
When you have collected more references, please feel encouraged to add them to that list there...
answered Oct 20, 2009 at 9:23
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$\begingroup$ Thanks! I wasn't aware of that survey, although I guess after all this talk about nLab/mathflow I should have known to check there first before posting my question. $\endgroup$ Commented Oct 20, 2009 at 9:32
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$\begingroup$ In fact, I started expanded that entry and added that reference only after having seen your question here. So you wouldn't have found it before. See, I always feel that just posting an answer here is a bit of a waste of energy, as it will just eventually disappear in noise. I'd much rather give the answer in a stable place such as a wiki, and then just point to that from here. That seems to be much more efficient and sustainable. $\endgroup$ Commented Oct 27, 2009 at 16:44
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- D. Leites, Lie superalgebras, J. Soviet Math. 30 (1985), 2481-2512 [http://dx.doi.org/10.1007/BF02249121 ] - a survey.
- M. Scheunert, The theory of Lie superalgebras. An introduction, Lect. Notes Math. 716 (1979) [should be available online].
answered Nov 1, 2009 at 13:19
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I like the book Varadarajan: "Supersymmetry for Mathematicians: An Introduction", but that tries to explain different aspects of supersymmetry used by physicists besides Lie superalgebras you may or may not be interested in.
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For a quick, self-learning introduction you can take a look at Alberto Elduque's talks and papers in
starting first with the talk called "Simple modular Lie superalgebras; Encuentro Matemático Hispano-Marroquí (Casablanca, 2008)."
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By request, I have moved Kaplansky's never-quite-published writings on Lie and Jordan superalgebras to one of my sites, in this case
http://zakuski.math.utsa.edu/~kap/superalgebra.html
I also posted some of his correspondence with Kevin McCrimmon
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The representation theory has been developed by a number of people, including Jon Brundan and Sasha Kleschchev at U. Oregon. Take a look at the publication list Brundan has (with PDF files) on his homepage: http://darkwing.uoregon.edu/~brundan/research.php
answered Mar 7, 2010 at 22:01