Matches in SemOpenAlex for { <https://semopenalex.org/work/W2799016545> ?p ?o ?g. }
Showing items 1 to 73 of
73
with 100 items per page.
- W2799016545 abstract "We give a criterion for the complete reducibility of modules satisfying a composability condition for a meromorphic open-string vertex algebra $V$ using the first cohomology of the algebra. For a $V$-bimodule $M$, let $hat{H}^{1}_{infty}(V, M)$ be the first cohomology of $V$ with the coefficients in $M$. Let $hat{Z}^{1}_{infty}(V, M)$ be the subspace of $hat{H}^{1}_{infty}(V, M)$ canonically isomorphic to the space of derivations obtained from the zero mode of the right vertex operators of weight $1$ elements such that the difference between the skew-symmetric opposite action of the left action and the right action on these elements are Laurent polynomials in the variable. If $hat{H}^{1}_{infty}(V, M)= hat{Z}^{1}_{infty}(V, M)$ for every $Z$-graded $V$-bimodule $M$, then every left $V$-module satisfying a composability condition is completely reducible. In particular, since a lower-bounded $Z$-graded vertex algebra $V$ is a special meromorphic open-string vertex algebra and left $V$-modules are in fact what has been called generalized $V$-modules with lower-bounded weights (or lower-bounded generalized $V$-modules), this result provides a cohomological criterion for the complete reducibility of lower-bounded generalized modules for such a vertex algebra. We conjecture that the converse of the main theorem above is also true. We also prove that when a grading-restricted vertex algebra $V$ contains a subalgebra satisfying some familiar conditions, the composability condition for grading-restricted generalized $V$-modules always holds and we need $hat{H}^{1}_{infty}(V, M)= hat{Z}^{1}_{infty}(V, M)$ only for every $Z$-graded $V$-bimodule $M$ generated by a grading-restricted subspace in our complete reducibility theorem." @default.
- W2799016545 created "2018-05-07" @default.
- W2799016545 creator A5066095681 @default.
- W2799016545 creator A5086540102 @default.
- W2799016545 date "2018-04-19" @default.
- W2799016545 modified "2023-10-12" @default.
- W2799016545 title "The first cohomology, derivations and the reductivity of a (meromorphic open-string) vertex algebra" @default.
- W2799016545 cites W1486434117 @default.
- W2799016545 cites W1999758812 @default.
- W2799016545 cites W2069505104 @default.
- W2799016545 cites W2130139996 @default.
- W2799016545 cites W2908411982 @default.
- W2799016545 cites W2962801575 @default.
- W2799016545 cites W2963147989 @default.
- W2799016545 cites W2963369432 @default.
- W2799016545 doi "https://doi.org/10.48550/arxiv.1804.07423" @default.
- W2799016545 hasPublicationYear "2018" @default.
- W2799016545 type Work @default.
- W2799016545 sameAs 2799016545 @default.
- W2799016545 citedByCount "0" @default.
- W2799016545 crossrefType "posted-content" @default.
- W2799016545 hasAuthorship W2799016545A5066095681 @default.
- W2799016545 hasAuthorship W2799016545A5086540102 @default.
- W2799016545 hasBestOaLocation W27990165451 @default.
- W2799016545 hasConcept C100376341 @default.
- W2799016545 hasConcept C114614502 @default.
- W2799016545 hasConcept C118615104 @default.
- W2799016545 hasConcept C132525143 @default.
- W2799016545 hasConcept C134306372 @default.
- W2799016545 hasConcept C135658033 @default.
- W2799016545 hasConcept C136119220 @default.
- W2799016545 hasConcept C14394260 @default.
- W2799016545 hasConcept C179724543 @default.
- W2799016545 hasConcept C202444582 @default.
- W2799016545 hasConcept C33923547 @default.
- W2799016545 hasConcept C34388435 @default.
- W2799016545 hasConcept C67996461 @default.
- W2799016545 hasConcept C78606066 @default.
- W2799016545 hasConcept C80899671 @default.
- W2799016545 hasConceptScore W2799016545C100376341 @default.
- W2799016545 hasConceptScore W2799016545C114614502 @default.
- W2799016545 hasConceptScore W2799016545C118615104 @default.
- W2799016545 hasConceptScore W2799016545C132525143 @default.
- W2799016545 hasConceptScore W2799016545C134306372 @default.
- W2799016545 hasConceptScore W2799016545C135658033 @default.
- W2799016545 hasConceptScore W2799016545C136119220 @default.
- W2799016545 hasConceptScore W2799016545C14394260 @default.
- W2799016545 hasConceptScore W2799016545C179724543 @default.
- W2799016545 hasConceptScore W2799016545C202444582 @default.
- W2799016545 hasConceptScore W2799016545C33923547 @default.
- W2799016545 hasConceptScore W2799016545C34388435 @default.
- W2799016545 hasConceptScore W2799016545C67996461 @default.
- W2799016545 hasConceptScore W2799016545C78606066 @default.
- W2799016545 hasConceptScore W2799016545C80899671 @default.
- W2799016545 hasLocation W27990165451 @default.
- W2799016545 hasLocation W27990165452 @default.
- W2799016545 hasLocation W27990165453 @default.
- W2799016545 hasOpenAccess W2799016545 @default.
- W2799016545 hasPrimaryLocation W27990165451 @default.
- W2799016545 hasRelatedWork W1803068283 @default.
- W2799016545 hasRelatedWork W1967149041 @default.
- W2799016545 hasRelatedWork W2008731611 @default.
- W2799016545 hasRelatedWork W2056663089 @default.
- W2799016545 hasRelatedWork W2508984732 @default.
- W2799016545 hasRelatedWork W2912064042 @default.
- W2799016545 hasRelatedWork W2950061627 @default.
- W2799016545 hasRelatedWork W2951565676 @default.
- W2799016545 hasRelatedWork W4298372416 @default.
- W2799016545 hasRelatedWork W776536739 @default.
- W2799016545 isParatext "false" @default.
- W2799016545 isRetracted "false" @default.
- W2799016545 magId "2799016545" @default.
- W2799016545 workType "article" @default.