10 citations · 10 across the 7 of their papers we have counts for
7 papers
Lie-Rinehart and Poisson algebras over -rings
Eugene Lerman, Ruben Louis
We define the analogue of Lie-Rinehart algebras over -rings. We show that given a Poisson -ring its module of -Käh…
Poisson -schemes
Eugene Lerman
We introduce Poisson -rings and Poisson local -ringed spaces. We show that the spectrum of a Poisson -ring is an affine Poisson -scheme. We…
Vector fields and flows on -schemes
Eugene Lerman
We prove that a vector field on an affine -scheme Spec(A) has a flow if the -ring A is finitely generated. If the vector field is complete then the flow is the…
Cartan calculus for -ringed spaces
Eugene Lerman
In an earlier paper (arXiv:2212.11163) I constructed a complex of differential forms on a local -ringed space. In this paper I define a sheaf of vector fields (``the tang…
Toric symplectic singular spaces I: isolated singularities
D. Burns, V. Guillemin, E. Lerman
We generalize a theorem of Delzant classifying compact connected symplectic manifolds with completely integrable torus actions to certain singular symplectic spaces. The assumption…
Melrose--Uhlmann projectors, the metaplectic representation and symplectic cuts
V. Guillemin, E. Lerman
By applying the symplectic cutting operation to cotangent bundles, one can construct a large number of interesting symplectic cones. In this paper we show how to attach algebras of…