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10 papers
Leibniz Cohomology and Connections on Differentiable Manifolds
Jerry Lodder
We show how an affine connection on a Riemannian manifold occurs naturally as a cochain in the complex for Leibniz cohomology of vector fields with coefficients in the adjoint repr…
Hochschild and Simplicial Cohomology
Jerry Lodder
We study a naturally occurring -subalgebra of the full -Hochschild cochain complex arising from coherent cochains. For group rings and certain category algebras, t…
Hochschild cochains as a Frobenius algebra
Jerry Lodder
We construct a Frobenius algebra structure on the Hochschild cochains of a group ring k[G] that extends the known structure of a <1, 2> topological quantum field theory on HH^0(k[G…
A Comparison of Products in Hochschild Cohomology
Jerry Lodder
We transport Steenrod's cup-i products from the singular cochains on the free loop space Maps(S^1, BG) to Hochschild's original cochain complex Hom (k[G]^*, k[G]) defining Hochschi…
A Structure Theorem for Leibniz Homology
Jerry Lodder
Presented is a structure theorem for the Leibniz Homology, HL_*, of an Abelian extension of a simple real Lie algebra g. As applications, results are stated for affine extensions o…
A Characteristic Map for Symplectic Manifolds
Jerry Lodder
We construct a local characteristic map to a symplectic manifold M via certain cohomology groups of Hamiltonian vector fields. For each p in M, the Leibniz cohomology of the Hamilt…