Hochschild Dglas and Torsion Algebras

Nonassociative Algebras: a Framework for Differential Geometry

A nonassociative algebra endowed with a Lie bracket, called a torsion algebra, is viewed as an algebraic analog of a manifold with an affine connection. Its elements are interpreted as vector fields and its multiplication is interpreted as a connection. This provides a framework for differential geometry on a formal manifold with a formal connection. A torsion algebra is a natural generalizatio...

Second Hochschild Cohomology of Convolution Algebras

Massey Products and Deformations

It is common knowledge that the construction of one-parameter deformations of various algebraic structures, like associative algebras or Lie algebras, involves certain conditions on cohomology classes, and that these conditions are usually expressed in terms of Massey products, or rather Massey powers. The cohomology classes considered are those of certain differential graded Lie algebras (DGLA...

Semicosimplicial Dglas in Deformation Theory

We describe a canonical L∞ structure on the total complex of a semicosimplicial differential graded Lie algebra and give an explicit descriprion of the Maurer-Cartan elements and of the associated deformation functor in the particular case of semicosimplicial Lie algebras. We use these results to investigate the deformation functor associated to a sheaf of Lie algebras L and to show that it is ...

Hochschild homology of preprojective algebras over the integers

We determine the Z-module structure and explicit bases for the preprojective algebra Π and all of its Hochschild (co)homology, for any non-Dynkin quiver. This answers (and generalizes) a conjecture of Hesselholt and Rains, producing new p-torsion elements in degrees 2p, l ≥ 1. We relate these elements by p-th power maps and interpret them in terms of the kernel of Verschiebung maps from noncomm...