Direct limit completions of vertex tensor categories

نویسندگان

چکیده

We show that direct limit completions of vertex tensor categories inherit and braided category structures, under conditions hold for example all known Virasoro affine Lie algebra categories. A consequence is the theory operator (super)algebra extensions also applies to infinite-order extensions. As an application, we relate rigid non-degenerate certain modules both superalgebra $\mathfrak{osp}(1|2)$ $N=1$ super via cosets.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Affine Lie algebras and vertex tensor categories

In this paper, we apply the general theory of tensor products of modules for a vertex operator algebra developed in [HL1]–[HL6] and [H1]–[H2] to the case of the Wess-Zumino-Novikov-Witten models (WZNW models) and related models in conformal field theory. Together with these papers, this paper, among other things, completes the solution of the open problem of constructing the desired braided ten...

متن کامل

Representations of vertex operator algebras and braided finite tensor categories

We discuss what has been achieved in the past twenty years on the construction and study of a braided finite tensor category structure on a suitable module category for a suitable vertex operator algebra. We identify the main difficult parts in the construction, discuss the methods developed to overcome these difficulties and present some further problems that still need to be solved. We also c...

متن کامل

Vertex operator algebras, the Verlinde conjecture, and modular tensor categories.

Let V be a simple vertex operator algebra satisfying the following conditions: (i) V(n)) = 0 for n < 0, V(0)=C1, and the contragredient module V' is isomorphic to V as a V-module; (ii) every N-gradable weak V-module is completely reducible; (iii) V is C(2)-cofinite. We announce a proof of the Verlinde conjecture for V, that is, of the statement that the matrices formed by the fusion rules among...

متن کامل

Formal Completions and Idempotent Completions of Triangulated Categories of Singularities

The main goal of this paper is to prove that the idempotent completions of the triangulated categories of singularities of two schemes are equivalent if the formal completions of these schemes along singularities are isomorphic. We also discuss Thomason theorem on dense subcategories and a relation to the negative K-theory.

متن کامل

Tensor Products of Modules for a Vertex Operator Algebra and Vertex Tensor Categories Yi-zhi Huang and James Lepowsky

In this paper, we present a theory of tensor products of classes of modules for a vertex operator algebra. We focus on motivating and explaining new structures and results in this theory, rather than on proofs, which are being presented in a series of papers beginning with [HL4] and [HL5]. An announcement has also appeared [HL1]. The theory is based on both the formal-calculus approach to verte...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Communications in Contemporary Mathematics

سال: 2021

ISSN: ['0219-1997', '1793-6683']

DOI: https://doi.org/10.1142/s0219199721500334