Tangent and Cotangent Lifts and Graded Lie Algebras Associated with Lie Algebroids |
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Authors: | J Grabowski P Urbański |
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Institution: | (1) Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland;(2) Mathematical Institute, Polish Academy of Sciences, niadeckich 8, P.O. Box 137, 00-950 Warsaw, Poland;(3) Division of Mathematical Methods in Physics, University of Warsaw, Hoa 74, 00-682 Warsaw, Poland |
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Abstract: | Generalized Schouten, Frölicher–Nijenhuis and Frölicher–Richardson brackets are defined for an arbitrary Lie algebroid. Tangent and cotangent lifts of Lie algebroids are introduced and discussed and the behaviour of the related graded Lie brackets under these lifts is studied. In the case of the canonical Lie algebroid on the tangent bundle, a new common generalization of the Frölicher–Nijenhuis and the symmetric Schouten brackets, as well as embeddings of the Nijenhuis–Richardson and the Frölicher–Nijenhuis bracket into the Schouten bracket, are obtained. |
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Keywords: | cotangent lift Frö licher– Nijenhuis bracket Lie algebroid Poisson structure Schouten bracket tangent lift |
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