Details

Autor(en) / Beteiligte

• Boe, Brian D
• Kujawa, Jonathan R
• Nakano, Daniel K

Titel

Complexity for modules over the classical Lie superalgebra gl(m|n)

Ist Teil von

• Compositio mathematica, 2012-09, Vol.148 (5), p.1561

Ort / Verlag

London: Cambridge University Press

Erscheinungsjahr

2012

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Abstract Let ${\Xmathfrak g}={\Xmathfrak g}_{\zerox }\oplus {\Xmathfrak g}_{\onex }$ be a classical Lie superalgebra and let F be the category of finite-dimensional ${\Xmathfrak g}$ -supermodules which are completely reducible over the reductive Lie algebra ${\Xmathfrak g}_{\zerox }$ . In [B. D. Boe, J. R. Kujawa and D. K. Nakano, Complexity and module varieties for classical Lie superalgebras, Int. Math. Res. Not. IMRN (2011), 696-724], we demonstrated that for any module M in the rate of growth of the minimal projective resolution (i.e. the complexity of M) is bounded by the dimension of ${\Xmathfrak g}_{\onex }$ . In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\Xmathfrak {gl}(m|n)$ . In both cases we show that the complexity is related to the atypicality of the block containing the module. [PUBLICATION ABSTRACT]