Skip Navigation



Proceedings of the London Mathematical Society Advance Access published online on May 2, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn019
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Boe, B. D.
Right arrow Articles by Nakano, D. K.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

Cohomology and support varieties for Lie superalgebras II

Brian D. Boe

Department of Mathematics
University of Georgia
Athens, GA 30602
USA
brian@math.uga.edu

Jonathan R. Kujawa

Department of Mathematics
University of Oklahoma
Norman, OK 73019
USA
kujawa@math.ou.edu

Daniel K. Nakano

Department of Mathematics
University of Georgia
Athens, GA 30602
USA

Received 15 August 2007. Revision received 14 February 2008.

In [2] (Preprint, 2006, arXiv:math.RT/0609363) the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra, and the dimension of the support variety for a simple supermodule was conjectured to equal the atypicality of the supermodule. In this paper the authors compute the support varieties of Kac supermodules for Type-I Lie superalgebras and of the simple supermodules for Formula (m|n). The latter result verifies our earlier conjecture for Formula (m|n). In our investigation we also delineate several of the major differences between Type-I versus Type-II classical Lie superalgebras. Finally, the connection between atypicality, defect and superdimension is made more precise by using the theory of support varieties and representations of Clifford superalgebras.

The second author was partially supported by NSF grants DMS-0402916 and DMS-0734226, and the third author was partially supported by NSF grants DMS-0400548 and DMS-0654169.

2000 Mathematics Subject Classification 17B56, 17B10 (primary), 13A50 (secondary).


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.