A ug 2 00 2 The Lie algebra cohomology of jets ∗
نویسنده
چکیده
Let g be a finite-dimensional complex reductive semi simple Lie algebra. We present a new calculation of the continuous cohomology of the Lie algebra zg[[z]]. In particular, we shall give an explicit formula for the Laplacian on the Lie algebra cochains, from which we can deduce that the cohomology in each dimension is a finite-dimensional representation of g which contains any irreducible representation of g at most once.
منابع مشابه
Hamiltonian type Lie bialgebras
X iv :m at h/ 06 05 66 9v 9 [ m at h. R A ] 1 5 A ug 2 00 6 Hamiltonian type Lie bialgebras Bin Xin , Guang’ai Song , Yucai Su 3) 1)Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China 2)College of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai, Shandong 264005, China 3)Department of Mathematics, University of Science and T...
متن کاملA ug 2 00 0 HOMOLOGY OF COMPLETE SYMBOLS AND NON - COMMUTATIVE GEOMETRY
We identify the periodic cyclic homology of the algebra of complete symbols on a differential groupoid G in terms of the cohomology of S * (G), the cosphere bundle of A(G), where A(G) is the Lie algebroid of G. We also relate the Hochschild homology of this algebra with the homogeneous Poisson homology of the space A * (G) 0 ∼ = S * (G) × (0, ∞), the dual of A(G) with the zero section removed. ...
متن کاملJu l 2 00 6 GELFAND - FUCHS COHOMOLOGY OF INVARIANT FORMAL VECTOR FIELDS
Let Γ be a finite group acting linearly on a vector space V . We compute the Lie algebra cohomology of the Lie algebra of Γ-invariant formal vector fields on V . We use this computation to define characteristic classes for foliations on orbifolds.
متن کاملThe Lie algebra cohomology of jets
Let g be a finite-dimensional complex reductive semi simple Lie algebra. We present a new calculation of the continuous cohomology of the Lie algebra zg[[z]]. In particular, we shall give an explicit formula for the Laplacian on the Lie algebra cochains, from which we can deduce that the cohomology in each dimension is a finite-dimensional representation of g which contains any irreducible repr...
متن کاملar X iv : m at h / 06 08 39 5 v 1 [ m at h . Q A ] 1 5 A ug 2 00 6 CHARACTERISTIC CLASSES OF A ∞ - ALGEBRAS
A standard combinatorial construction, due to Kontsevich, associates to any A∞-algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We describe an alternative version of this construction based on noncommutative geometry and use it to prove that homotopy equivalent algebras give rise to the same cohomology...
متن کامل