DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Logarithmic generalized module

Definition

A logarithmic module for a conformal vertex algebra of CFT type is a grading-restricted generalized module, as in Grading-restricted generalized module, on which $L_{M} (0)$ is not semisimple. Equivalently, some generalized weight space contains $m$ and $h \in C$ with $(L_{M} (0) - h)^{r} m = 0$ and $(L_{M} (0) - h)^{r - 1} m \neq 0$ for an integer $r \geq 2$ . This definition records the Jordan-block condition; it does not assert that a named vertex algebra has such a module or that its module category has any particular tensor, finite-length, or modular property.

Depends on

Grading-restricted generalized module

Used by

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Yi-Zhi Huang, James Lepowsky, and Lin Zhang, Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I, Definition 2.12 and §§1.1–1.2 (standard reference, not scraped)
Dražen Adamović and Antun Milas, Lattice Construction of Logarithmic Modules for Certain Vertex Algebras, §2 (standard reference, not scraped)