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In this
article, we want to generalize the concept of the Lie algebra of vector
fields. For this, in section 2, we define the concept of T−bundle which is a canonical generalization of
the tangent bundle and define the category of such objects. In section 3,
the T−bundle Lb i=1
TM, and is defined and showed that any T−bundle
is isomorphic to a suitable Lb i=1 TM, for some
b. Then, by defining the multiplication and bracket on the space of
sections of T−bundle Lb i=1 TM, we put multiplication and bracket for smooth
sections of an arbitrary T−bundle; and
show that the set of all smooth sections of a T−bundle
with these multiplication and bracket and also with point-wise addition
and scaler product, forms a Lie algebra.
Url: http://www.iust.ac.ir/ijesen/article-A-10-1-138-1-en.html
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