Universal central extensions of slm|n over Z/2Z-graded algebras
Document Type
Article
Publication Date
9-2015
Department
Department of Mathematical Sciences
Abstract
We study central extensions of the Lie superalgebra sl m|n (A), where A is a Z/2Z-graded superalgebra over a commutative ring K. The Steinberg Lie superalgebra st m|n (A) plays a crucial role. We show that st m|n (A) is a central extension of sl m|n (A) for m+n≥3. We use a Z/2Z-graded version of cyclic homology to show that the center of the extension is isomorphic to HC 1 (A) as K-modules. For m+n≥5, we prove that st m|n (A) is the universal central extension of sl m|n (A). For m+n=3, 4, we prove that st 2|1 (A) and st 3|1 (A) are both centrally closed. The universal central extension of st 2|2 (A) is constructed explicitly.
Publication Title
Journal of Pure and Applied Algebra
Recommended Citation
Chen, H.,
&
Sun, J.
(2015).
Universal central extensions of slm|n over Z/2Z-graded algebras.
Journal of Pure and Applied Algebra,
219(9), 4278-4294.
http://doi.org/10.1016/j.jpaa.2015.02.018
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6794
Publisher's Statement
Corrigendum: https://doi.org/10.1016/j.jpaa.2015.08.001