Contractions: Nijenhuis and Saletan tensors for general algebraic structures

Details Contractions: Nijenhuis and Saletan tensors for general algebraic structures Contractions: Nijenhuis and Saletan tensors for general algebraic structures

2001-03-16

arxiv.org/abs/math/0103103v2

J. Phys. A: Math. Gen. 34 (2001), 3769-3789.

Mathematics

Differential Geometry

25 pages, LateX, corrected typos

Scientific paper

10.1088/0305-4470/34/18/306

Generalizations in many directions of the contraction procedure for Lie algebras introduced by E.J.Saletan are proposed. Products of arbitrary nature, not necessarily Lie brackets, are considered on sections of finite-dimensional vector bundles. Saletan contractions of such infinite-dimensional algebras are obtained via a generalization of the Nijenhuis tensor approach. In particular, this procedure is applied to Lie algebras, Lie algebroids, and Poisson structures. There are also results on contractions of n-ary products and coproducts.

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