The symplectic fermion ribbon quasi-Hopf algebra and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>S</mml:mi><mml:mi>L</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-action on its centre

We introduce a family of factorisable ribbon quasi-Hopf algebras Q(N) for N positive integer: as an algebra, is the semidirect product CZ2 with direct sum Graßmann and Clifford algebra in 2N generators. show that RepQ(N) equivalent to symplectic fermion category SF(N) was computed [54] from conformal blocks corresponding logarithmic field theory. The latter turn conjecturally representations Vev, even part vertex operator super algebra. Using formalism developed [20] we compute projective SL(2,Z)-action on centre obtained Lyubashenko's general theory mapping class group actions finite categories. This allows us test conjectural non-semisimple version modular Verlinde formula: verify agrees projectively pseudo trace functions Vev.