arXiv subjects

Frank Keller

Publications and source records attributed to Frank Keller.

57 records · Page 4Linked to original sources

arXiv2006

Formal Deformations of Dirac Structures

In this paper we set-up a general framework for a formal deformation theory of Dirac structures. We give a parameterization of formal deformations in terms of two-forms obeying a cubic equation. The notion of equivalence is discussed in detail. We show that the obstruction for the construction of deformations order by order lies in the third Lie algebroid cohomology of the Dirac structure. However, the classification of inequivalent first order deformations is not given by the second Lie algebroid cohomology but turns out to be more complicated.

math.QA↗

arXiv2005

Deformation von Lie-Algebroiden und Dirac-Strukturen

In this diploma thesis we discuss the deformation theory of Lie algebroids and Dirac structures. The first chapter gives a short introduction to Dirac structures on manifolds as introduced by Courant in 1990. We also give some physical applications of Dirac structures. In the second chapter we present the deformation theory of Lie algebroids following a recent work of Crainic and Moerdijk. We discuss the subject from three different points of view and show the equivalence of these different interpretations. In the third chapter we give definitions for smooth and formal deformations of Dirac structures on Courant algebroids. To investigate the formal theory, we write the Courant bracket with the use of the Rothstein super-Poisson bracket as a derived bracket. As the main result we show that the obstruction for extending a given formal deformation of a certain order lies in the third Lie algebroid cohomology of the Lie algebroid given by the undeformed Dirac structure.

math-ph↗

arXiv1995

Towards an Account of Extraposition in HPSG

This paper investigates the syntax of extraposition in the HPSG framework. We present English and German data (partly taken from corpora), and provide an analysis using lexical rules and a nonlocal dependency. The condition for binding this dependency is formulated relative to the antecedent of the extraposed phrase, which entails that no fixed site for extraposition exists. Our analysis accounts for the interaction of extraposition with fronting and coordination, and predicts constraints on multiple extraposition.

cmp-lg↗