# The N=1 triplet vertex operator superalgebras - Mathematics > Quantum Algebra

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Abstract: We introduce a new family of C 2-cofinite N=1 vertex operator superalgebrasSWm, $m \geq 1$, which are natural super analogs of the triplet vertexalgebra family Wp, $p \geq 2$, important in logarithmic conformal fieldtheory. We classify irreducible SWm-modules and discuss logarithmic modules.We also compute bosonic and fermionic formulas of irreducible SWm characters.Finally, we contemplate possible connections between the category ofSWm-modules and the category of modules for the quantum groupU^{small} qsl 2, q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily onproperties of characters and the Zhu-s algebra ASWm. This paper is acontinuation of arXiv:0707.1857.