Matches in SemOpenAlex for { <https://semopenalex.org/work/W2907389506> ?p ?o ?g. }
- W2907389506 abstract "Given a double vector bundle $Dto M$, we define a bigraded `Weil algebra' $mathcal{W}(D)$, which `realizes' the algebra of smooth functions on the supermanifold $D[1,1]$. We describe in detail the relations between the Weil algebras of $D$ and those of the double vector bundles $D', D$ obtained by duality operations. In particular, we show that double-linear Poisson structures on $D$ can be described alternatively as Gerstenhaber brackets on $mathcal{W}(D)$, vertical differentials on $mathcal{W}(D')$, or horizontal differentials on $mathcal{W}(D)$. We also give a new proof of Voronov's result characterizing double Lie algebroid structures. In the case that $D=TA$ is the tangent prolongation of a Lie algebroid, we find that $mathcal{W}(D)$ is the Weil algebra of the Lie algebroid, as defined by Mehta and Abad-Crainic. We show that the deformation complex of Lie algebroids, the theory of IM forms and IM multivector fields, and 2-term representations up to homotopy all have natural interpretations in terms of our Weil algebras." @default.
- W2907389506 created "2019-01-11" @default.
- W2907389506 creator A5055593599 @default.
- W2907389506 creator A5064122261 @default.
- W2907389506 date "2019-01-02" @default.
- W2907389506 modified "2023-09-27" @default.
- W2907389506 title "The Weil algebra of a double Lie algebroid" @default.
- W2907389506 cites W1529287742 @default.
- W2907389506 cites W1532154335 @default.
- W2907389506 cites W1570119228 @default.
- W2907389506 cites W1591200122 @default.
- W2907389506 cites W1664654057 @default.
- W2907389506 cites W1742104850 @default.
- W2907389506 cites W1963488414 @default.
- W2907389506 cites W1970900656 @default.
- W2907389506 cites W1975666635 @default.
- W2907389506 cites W1987511575 @default.
- W2907389506 cites W1994243491 @default.
- W2907389506 cites W2030364524 @default.
- W2907389506 cites W2036954048 @default.
- W2907389506 cites W2039011617 @default.
- W2907389506 cites W2048172663 @default.
- W2907389506 cites W2048468810 @default.
- W2907389506 cites W2060951988 @default.
- W2907389506 cites W2062621534 @default.
- W2907389506 cites W2064814872 @default.
- W2907389506 cites W2087396948 @default.
- W2907389506 cites W2088425722 @default.
- W2907389506 cites W2134034177 @default.
- W2907389506 cites W2149568383 @default.
- W2907389506 cites W2166228888 @default.
- W2907389506 cites W2247076017 @default.
- W2907389506 cites W2549055881 @default.
- W2907389506 cites W2746546518 @default.
- W2907389506 cites W2890243073 @default.
- W2907389506 cites W2900386963 @default.
- W2907389506 cites W2963994074 @default.
- W2907389506 cites W3000526647 @default.
- W2907389506 cites W3101117123 @default.
- W2907389506 cites W3102040445 @default.
- W2907389506 cites W3103061608 @default.
- W2907389506 cites W3103217216 @default.
- W2907389506 cites W3103891335 @default.
- W2907389506 cites W3106429792 @default.
- W2907389506 cites W3187248183 @default.
- W2907389506 cites W99483571 @default.
- W2907389506 hasPublicationYear "2019" @default.
- W2907389506 type Work @default.
- W2907389506 sameAs 2907389506 @default.
- W2907389506 citedByCount "1" @default.
- W2907389506 countsByYear W29073895062019 @default.
- W2907389506 crossrefType "posted-content" @default.
- W2907389506 hasAuthorship W2907389506A5055593599 @default.
- W2907389506 hasAuthorship W2907389506A5064122261 @default.
- W2907389506 hasConcept C136119220 @default.
- W2907389506 hasConcept C14344131 @default.
- W2907389506 hasConcept C157157409 @default.
- W2907389506 hasConcept C169654258 @default.
- W2907389506 hasConcept C202444582 @default.
- W2907389506 hasConcept C203946495 @default.
- W2907389506 hasConcept C2776503324 @default.
- W2907389506 hasConcept C28903235 @default.
- W2907389506 hasConcept C33923547 @default.
- W2907389506 hasConcept C51568863 @default.
- W2907389506 hasConcept C73648015 @default.
- W2907389506 hasConcept C95857938 @default.
- W2907389506 hasConceptScore W2907389506C136119220 @default.
- W2907389506 hasConceptScore W2907389506C14344131 @default.
- W2907389506 hasConceptScore W2907389506C157157409 @default.
- W2907389506 hasConceptScore W2907389506C169654258 @default.
- W2907389506 hasConceptScore W2907389506C202444582 @default.
- W2907389506 hasConceptScore W2907389506C203946495 @default.
- W2907389506 hasConceptScore W2907389506C2776503324 @default.
- W2907389506 hasConceptScore W2907389506C28903235 @default.
- W2907389506 hasConceptScore W2907389506C33923547 @default.
- W2907389506 hasConceptScore W2907389506C51568863 @default.
- W2907389506 hasConceptScore W2907389506C73648015 @default.
- W2907389506 hasConceptScore W2907389506C95857938 @default.
- W2907389506 hasLocation W29073895061 @default.
- W2907389506 hasOpenAccess W2907389506 @default.
- W2907389506 hasPrimaryLocation W29073895061 @default.
- W2907389506 hasRelatedWork W1595869386 @default.
- W2907389506 hasRelatedWork W1614413831 @default.
- W2907389506 hasRelatedWork W1764500480 @default.
- W2907389506 hasRelatedWork W1766982745 @default.
- W2907389506 hasRelatedWork W1771949607 @default.
- W2907389506 hasRelatedWork W1819359804 @default.
- W2907389506 hasRelatedWork W2017200202 @default.
- W2907389506 hasRelatedWork W2087816010 @default.
- W2907389506 hasRelatedWork W2134034177 @default.
- W2907389506 hasRelatedWork W2136177497 @default.
- W2907389506 hasRelatedWork W2141087342 @default.
- W2907389506 hasRelatedWork W2144291669 @default.
- W2907389506 hasRelatedWork W2497227697 @default.
- W2907389506 hasRelatedWork W2950596696 @default.
- W2907389506 hasRelatedWork W2963235537 @default.
- W2907389506 hasRelatedWork W2964104643 @default.
- W2907389506 hasRelatedWork W2997198201 @default.
- W2907389506 hasRelatedWork W2999026187 @default.
- W2907389506 hasRelatedWork W3126039438 @default.