ar X iv : m at h / 06 03 73 3 v 2 [ m at h . A C ] 1 9 Ju n 20 06 RIGID COMPLEXES VIA DG ALGEBRAS

ar X iv : m at h / 06 03 73 3 v 1 [ m at h . A C ] 3 1 M ar 2 00 6 RIGID COMPLEXES VIA DG ALGEBRAS

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...

ar X iv : m at h / 06 03 73 3 v 3 [ m at h . A C ] 1 8 D ec 2 00 6 RIGID COMPLEXES VIA DG ALGEBRAS

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...

ar X iv : m at h / 06 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE

ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n

We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1

ar X iv : m at h / 03 06 23 5 v 1 [ m at h . D G ] 1 6 Ju n 20 03 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY JØRGEN

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [48] and [51] by a certain fractional power of the abelian theory first considered in [32] and further studied in [2].