We prove Feigin-Frenkel type dualities between subregular W-algebras of A,B and principal W-superalgebras sl(1|n),osp(2|2n). The A case proves a conjecture Feigin Semikhatov. Let (g1,g2)=(sln+1,sl(1|n+1)) or (so2n+1,osp(2|2n)) let r be the lacity g1. k complex number ? defined by r(k+h1?)(?+h2?)=1 with hi? dual Coxeter numbers gi. Our first main result is that Heisenberg cosets Ck(g1) C?(g2) th...

Abstract The rank 1 bosonic ghost vertex algebra, also known as the $$\beta \gamma $$ ? ? ghosts, symplectic bosons or Weyl is a simple example of conformal field theory which neither rational, nor $$C_2$$ C 2 -co...

It is proved that any vertex operator algebra for which the image of the Virasoro element in Zhu’s algebra is algebraic over complex numbers is finitely generated. In particular, any vertex operator algebra with a finite dimensional Zhu’s algebra is finitely generated. As a result, any rational vertex operator algebra is finitely generated. Although many well known vertex operator algebras are ...

This dissertation investigates a new approach to query languages inspired by structural recursion and by the categorical notion of a monad. A language based on these principles has been designed and studied. It is found to have the strength of several widely known relational languages but without their weaknesses. This language and its various extensions are shown to exhibit a conservative exte...