658 research outputs found
-term averaging -algebras and non-abelian extensions of averaging Lie algebras
In recent years, averaging operators on Lie algebras (also called embedding
tensors in the physics literature) and associated tensor hierarchies form an
efficient tool for constructing supergravity and higher gauge theories. A Lie
algebra with an averaging operator is called an averaging Lie algebra. In the
present paper, we introduce -term averaging -algebras and give
characterizations of some particular classes of such homotopy algebras. Next,
we study non-abelian extensions of an averaging Lie algebra by another
averaging Lie algebra. We define the second non-abelian cohomology group to
classify the equivalence classes of such non-abelian extensions. Next, given a
non-abelian extension of averaging Lie algebras, we show that the obstruction
for a pair of averaging Lie algebra automorphisms to be inducible can be seen
as the image of a suitable Wells map. Finally, we discuss the Wells short exact
sequence in the above context
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