Low-dimensional cohomology of current Lie algebras and analogs of the Riemann tensor for loop manifolds

Abstract

We obtain formulas for the first and second cohomology groups of a general current Lie algebra with coefficients in the "current" module, and apply them to compute structure functions for manifolds of loops with values in compact Hermitian symmetric spaces.

v8: cosmetic changes

References in corpus (2)

• The analogs of Riemann and Penrose tensors on supermanifolds
• The analogs of the Riemann tensor for exceptional structures on supermanifolds

Cited by in corpus (11)

• On $\delta$-derivations of Lie algebras and superalgebras
• Hom-Lie structures on Kac-Moody algebras
• A compendium of Lie structures on tensor products
• Deformations of current Lie algebras. I. Small algebras in characteristic 2
• Invariants of Lie algebras extended over commutative algebras without unit
• Melikyan algebra is a deformation of a Poisson algebra
• On contact brackets on the tensor product
• Lie algebras and around: selected questions
• On the algebras obtained by tensor product
• Commutative post-Lie algebra structures on Kac--Moody algebras
• The Automorphisms group of a Current Lie algebra