A common generalization of the Frölicher-Nijenhuis bracket and the Schouten bracket for symmetry multi vector fields

M. Dubois-Violette; P. W. Michor

paper

A common generalization of the Frölicher-Nijenhuis bracket and the Schouten bracket for symmetry multi vector fields

arXiv:alg-geom/9401006

Abstract

There is a canonical mapping from the space of sections of the bundle $\land T^{*} M \otimes S T M$ to $Ω (T^{*} M; T (T^{*} M))$ . It is shown that this is a homomorphism on $Ω (M; T M) f or t h e F r o ¨ l i c h er - N ij e nh u i s b r a c k e t s, an d a l soo n$ Γ(ST\ M) $f or t h e S c h o u t e nb r a c k e t o f sy mm e t r i c m u l t i v ec t or f i e l d s . B u tt h e w h o l e ima g e i s n o t a s u ba l g e b r a f or t h e F r o ¨ l i c h er - N ij e nh u i s b r a c k e t o n$ Ω(T^\ast M;T(T^\ast M))$.

14 pages, AMSTEX, LPTHE-ORSAY 94/05 and ESI 70 (1994)

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