This is a paper in a series to study quantum vertex algebras and their relations with various quantum algebras. In this paper, we introduce a notion of T-type quantum vertex algebra and a notion ofG-equivariant φ-coordinated quasi module for a T -type quantum vertex algebra with an automorphism group G. We refine and extend several previous results and we obtain a commutator formula for G-equiv...

We introduce a notion of φ-coordinated (quasi) module for a nonlocal vertex algebra and we establish a conceptual construction of nonlocal vertex algebras and their φ-coordinated (quasi) modules. As an application, we associate quantum affine algebras with weak quantum vertex algebras in the sense of [Li3], and we also associate a certain quantum βγ-system with quantum vertex algebras and φ-coo...

the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

We prove lifting results for DG modules that are akin to Auslander, Ding, and Solberg’s famous lifting results for modules. Introduction Convention. Throughout this paper, let R be a commutative noetherian ring. Hochster famously wrote that “life is really worth living” in a Cohen-Macaulay ring [7]. For instance, if R is Cohen-Macaulay and local with maximal regular sequence t, then R/(t) is ar...

The notion of a quasi-free Hilbert module over a function algebra A consisting of holomorphic functions on a bounded domain Ω in complex m space is introduced. It is shown that quasi-free Hilbert modules correspond to the completion of the direct sum of a certain number of copies of the algebra A. A Hilbert module is said to be weakly regular (respectively, regular) if there exists a module map...