Resumen de Cosets of Bershadsky–Polyakov algebras and rational W-algebras of type A

Tomoyuki Arakawa, Andrew R. Linshaw

• The Bershadsky–Polyakov algebra is the W-algebra associated to sl3 with its minimal nilpotent element fθ . For notational convenience we define W = W−3/2(sl3, fθ ). The simple quotient ofW is denoted byW, and for a positive integer,W is known to beC2-cofinite and rational.We prove that for all positive integers , W contains a rank one lattice vertex algebra VL , and that the coset C = Com(VL , W) is isomorphic to the principal, rational W(sl2)-algebra at level(2+3)/(2+1)−2. This was conjectured in the physics literature over 20 years ago. As a byproduct, we construct a new family of rational, C2-cofinite vertex superalgebras from W. Keywords Vert