We present new abelian partial difference sets and amorphic group schemes of both Latin square type and negative Latin square type in certain abelian p-groups. Our method is to construct what we call pseudo-quadratic bent functions and use them in place of quadratic forms. We also discuss a connection between strongly regular bent functions and amorphic group schemes.

We establish braided tensor equivalences among module categories over the twisted quantum double of a finite group defined by an extension of a group G by an abelian group, with 3-cocycle inflated from a 3-cocycle on G. We also prove that the canonical ribbon structure of the module category of any twisted quantum double of a finite group is preserved by braided tensor equivalences. We give two...

The nonabelian tensor square G⊗G of the group G is the group generated by the symbols g ⊗ h, where g, h ∈ G, subject to the relations gg′ ⊗ h = (gg′ ⊗ h)(g ⊗ h) and g ⊗ hh′ = (g ⊗ h)(g ⊗ hh′) for all g, g, h, h′ ∈ G, where gg′ = gg′g−1 is conjugation on the left. Following the work of C. Miller [18], R. K. Dennis in [10] introduced the nonabelian tensor square which is a specialization of the m...

Heckenberger introduced the Weyl groupoid of a finite-dimensional Nichols algebra diagonal type. We replace matrix its braiding by higher tensor and present construction which yields further groupoids. Abelian cohomology theory gives evidence for existence associated to such tensor.

LetM be a tensor category with coefficients in a fieldK of characteristic 0, that is, a K-linear pseudo-abelian symmetric monoidal category such that the tensor product ⊗ of M is bilinear. Then symmetric and exterior powers of an object M ∈ M make sense, by using appropriate projectors relative to the action of the symmetric groups on tensor powers of M . One may therefore introduce the zeta fu...

We outline a general construction applicable to the Turaev/Viro [TV], Crane/Yetter [CY] and generalized Turaev/Viro invariants (cf. [Y1]) of invariants valued in complex-valued functions on HD−2(M , GrC), where GrC is the abelian group of functorial tensor automorphisms on the artinian tortile category used to construct the TQFT. Introduction It is the purpose of this note to introduce a constr...

We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal categories. This establishes new tool the construction tensor As an example we obtain proofs several universal categories as conjectured by Deligne. Another constructs interesting in positive characteristic via tilting modules ${\rm SL}_2$ .

The asymptotic behaviour at late times of inhomogeneous axion-dilaton cosmologies is investigated. The space-times considered here admit two abelian space-like Killing vectors. These space-times evolve towards an anisotropic universe containing gravitational radiation. Furthermore, a peeling-off behaviour of the Weyl tensor and the antisymmetric tensor field strength is found. The relation to t...

2 Abelian groups 5 2.1 Stalks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Sheaf Hom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Tensor products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Inverse and Direct Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product H = H ⊗ · · ·⊗H is separable or entangled. We show that the tensor convolution ( φ . . . φ ) : G → H defined for mappings φ : G → H μ on an almost arbitrary locally compact abelian group G, give rise to formulation of an equivalent problem to the separability one.