Logarithmic (sl)over-cap(2) CFT models from Nichols algebras: I

被引：17

作者：

Semikhatov, A. M. ^{[1
]}

Tipunin, I. Yu ^{[1
]}

机构：

[1] Lebedev Phys Inst, Moscow 119991, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2013年 / 46卷 / 49期

关键词：

MINIMAL MODELS; BRAIDED GROUPS; FUSION; REPRESENTATIONS; EXTENSIONS; ROOT; CLASSIFICATION; MODULES; LIMIT;

D O I：

10.1088/1751-8113/46/49/494011

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We construct chiral algebras that centralize rank-2 Nichols algebras with at least one fermionic generator. This gives 'logarithmic' W-algebra extensions of a fractional-level (sl) over cap (2) algebra. We discuss crucial aspects of the emerging general relation between Nichols algebras and logarithmic conformal field theory (CFT) models: (i) the extra input, beyond the Nichols algebra proper, needed to uniquely specify a conformal model; (ii) a relation between the CFT counterparts of Nichols algebras connected by Weyl groupoid maps; and (iii) the common double bosonization U(X) of such Nichols algebras. For an extended chiral algebra, candidates for its simple modules that are counterparts of the U(X) simple modules are proposed, as a first step toward a functorial relation between U(X) and W-algebra representation categories.

引用

页数：53

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