We construct canonical integral transforms, analogous to the Fourier transform, that have periods six and three. The existence of this transform is shown to arise naturally from the expectation that the Schwartz space on the real line, viewed as the Heisenberg module of Rieffel and Connes over the rotation C*-algebra, should extend to a module action over the crossed product of the latter by th...

The notion of centrality for crossed modules was introduced by Norrie in her thesis [7], in which she studied the category of crossed modules CM from an algebraic point of view, showing suitable generalizations of group theoretic concepts and results. Subsequently, Norrie’s approach was followed by Carrasco, Cegarra and R.-Grandjeán. In [5] they proved that CM is an algebraic category (i.e. the...

A notion of generalized highest weight modules over the high rank Virasoro algebras is introduced in this paper, and a theorem, which was originally given as a conjecture by Kac over the Virasoro algebra, is generalized. Mainly, we prove that a simple Harish-Chandra module over a high rank Virasoro algebra is either a generalized highest weight module, or a module of the intermediate series.

Let (S,≤) be a strictly totally ordered monoid, R be a commutative ring and M be an R-module. We show the following results: (1) If (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a semi Hopfian [[RS,≤]]-module if and only if M is a semi Hopfian R-module; (2) If (S,≤) is artinian, then the generalized inverse polynomial module [MS,...

We introduce a hybrid backlight module, which consists of a hybrid light guide plate (HLGP) and a brightness enhancement film (BEF). The HLGP comprises functions of a conventional light guide plate, a reflector, and a BEF. The HLGP allows one-dimensional rays to be collimated. We add a BEF above the HLGP, and let the crossed-dimension rays to be collimated. Comparing with the conventional edge-...

We introduce a notion of strongly C×-graded, or equivalently, C/Zgraded generalized g-twisted V -module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V -module if V admits an additional C-grading compatible with g. Let V = ∐ n∈Z V(n) be a vertex operator algebra such that V(0)...

We extend our work in [1] to the case of Hopf comodule coalgebras. We introduce the cocylindrical module C♮H, where H is a Hopf algebra with bijective antipode and C is a Hopf comodule coalgebra over H. We show that there exists an isomorphism between the cocyclic module of the crossed coproduct coalgebra C>◭H and ∆(C♮H), the cocyclic module related to the diagonal of C♮H. We approximate HC(C >...