DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)verified 2026-11-04 (gpt-6.1-sol)

How statement and proof provenance work

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Regular conformal vertex algebra

Definition

A conformal vertex algebra $V$ of CFT type is regular when every weak $V$ -module is an algebraic direct sum of simple ordinary $V$ -submodules. Here weak means lower-truncated vertex-algebra module, simple means nonzero with no proper nonzero submodule, and ordinary means grading-restricted with semisimple $L_{0}$ . The zero module is the empty direct sum. Regularity concerns all weak modules; complete reducibility only for admissible modules is a separate, weaker property.

Definition references

Module for an ordinary vertex algebra

Ordinary module

Conformal vertex algebra of CFT type

Depends on

Dependency tree · 2 levels

Sources

Chongying Dong, Haisheng Li, and Geoffrey Mason, Regularity of Rational Vertex Operator Algebras