BFV-Complex and Higher Homotopy Structures

We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can be derived from the BFV-complex by means of homotopy transfer along contractions. Consequently the BFV-complex and the strong homotopy Lie algebroid structure are L ∞ quasi-isomorphic and control the same formal deformation problem. However there is a gap between the non-formal information encoded in the BFV-complex and in the strong homotopy Lie algebroid respectively. We prove that there is a one-to-one correspondence between coisotropic submanifolds given by graphs of sections and equivalence classes of normalized Maurer-Cartan elemens of the BFV-complex. This does not hold if one uses the strong homotopy Lie algebroid instea

Verification of Model Transformations

With the increasing use of automatic transformations of models, the correctness of these transformations becomes an increasingly important issue. Especially for model transformation generally defined using abstract description techniques like graph transformations or declarative relational specifications, however, establishing the soundness of those transformations by test-based approaches is not straight-forward. We show how formal verification of soundness conditions over such declarative relational style transformations can be performed using an interactive theorem prover. The relational style allows a direct translation of transformations as well as associated soundness conditions into corresponding axioms and theorems. Using the Isabelle theorem prover, the approach is demonstrated for a refactoring transformation and a connectedness soundness condition

Die Zyklen der Geschichte.\ud Passagen durch Schillers Wilhelm Tell

Schillers Dramen bergen komplexe Kompositionslinien, welche durch seine ästhetischen und geschichtsphilosophischen Ansätze geprägt sind. Gerade sein "Wilhelm Tell" kann durch eine Lesart, die versucht, seine strukturellen Aspekte unter Zuhilfenahme ausgewählter Konzepte zutage zu bringen, gewinnbringend gelesen werden. Auf diese Weise können einige Facetten des Dramas herausgearbeitet werden, die nicht offensichtlich sind

Special Section on Formal Methods for Industrial Critical Systems (Selected Papers from FMICS'11)

International audienceThis section contains extended versions of selected papers from the 16th International Workshop on Formal Methods for Industrial Critical Systems (FMICS'11)

The A∞ de Rham Theorem and Integration of Representations up to Homotopy

We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an functor from the representations up to homotopy of a Lie algebroid A to those of its infinity groupoid. This construction extends the usual integration of representations in Lie theory. We discuss several examples including Lie algebras and Poisson manifolds. The construction is based on an version of de Rham's theorem due to Gugenheim [15]. The integration procedure we explain here amounts to extending the construction of parallel transport for superconnections, introduced by Igusa [17] and Block-Smith [6], to the case of certain differential graded manifold

Deformations of Lie brackets and representations up to homotopy

We show that representations up to homotopy can be differentiated in a functorial way. A van Est type isomorphism theorem is established and used to prove a conjecture of Crainic and Moerdijk on deformations of Lie brackets.Comment: 28 page