2015/02/26 by Penkava, Michael, Pichereau, Anne
#13D10 #14B12 #14D15 #16E40 #16S80 #17B55 #17B70 #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1502.07503
We study \mathbb Z2-graded Poisson structures defined on \mathbb Z2-graded commutative polynomial algebras. In small dimensional cases, we exhibit classifications of such Poisson structures, obtain the associated Poisson \mathbb Z2-graded cohomology and in some cases, deformations of these Poisson brackets and P_∞-algebra structures. We highlight differences and analogies between this \mathbb Z2-graded context and the non graded context, by studying for example the links between Poisson cohomology and singularities.