Nijenhuis deformation of Gerstenhaber algebra and Poisson Quasi-Nijenhuis algebroids
 
 
Description:  The importance of Nijenhuis tensor on the Lie algebra of vector fields on a manifold is not only because of the Newlander-Nirenberg theorem, but also it appears in the study of Hamiltonian systems. The notion is known for some geometric structures such as Poisson manifolds, Courant algebroids, Omega-N-structures etc. On the other hand there are L-infinity-algebras associated to the mentioned structures. Since L-infinity-algebras are a generalization of Lie algebras, it is natural to ask what could be a good generalization of Nijenhuis tensor to the case of L-infinity?

In this talk, using a type of Richardson-Nijenhuis bracket on the space of vector valued forms on a graded vector space, we will see that Lie algebras are very particular cases of L-infinity-algebras. Then after recalling the notion of Nijenhuis tensor on a Lie algebra, I introduce (a type of) Nijenhuis on L-infinity-algebras. I will mention how the notion behaves well with the already existing notions of Nijenhuis on geometric structures. In particular, I will show that a Poisson Quasi-Nijenhuis structure with background is a nothing than a suitable choice of Nijenhuis deformation on some L-infinity-algebra.

Nijenhuis deformation of L-infinity-algebras enable us to construct new L-infinity-algebras. We will see this in the context of Gerstenhaber algebra, seen as L-infinity-algebra.

Date:  2016-04-27
Start Time:   11:30
Speaker:  Mohammad Jawad Azimi (CMUC/Univ. Coimbra)
Institution:  Centre for Mathematics of the University of Coimbra
Place:  Sala 5.5
Research Groups: -Geometry
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