The Lie algebra of cyclic coinvariants of a symplectic space

Coinvariants of Lie algebras of vector fields on algebraic varieties

We prove that the space of coinvariants of functions on an affine variety by a Lie algebra of vector fields whose flow generates finitely many leaves is finite-dimensional. Cases of the theorem include Poisson (or more generally Jacobi) varieties with finitely many symplectic leaves under Hamiltonian flow, complete intersections in Calabi-Yau varieties with isolated singularities under the flow of incompressible vector fields, quotients of Calabi-Yau varieties by finite volume-preserving groups under the incompressible vector fields, and arbitrary varieties with isolated singularities under th…

Poisson traces in positive characteristic

We study Poisson traces of the structure algebra A of an affine Poisson variety X defined over a field of characteristic p. According to arXiv:0908.3868v4, the dual space HP_0(A) to the space of Poisson traces arises as the space of coinvariants associated to a certain D-module M(X) on X. If X has finitely many symplectic leaves and the ground field has characteristic zero, then M(X) is holonomic, and thus HP_0(A) is finite dimensional. However, in characteristic p, the dimension of HP_0(A) is typically infinite. Our main results are complete computations of HP_0(A) for sufficiently large p wh…

余代数测量，循环理论和矩阵代数的同调

Coalgebra measurings, cyclic theory and homologies of matrix algebras

本文研究了余代数测量在代数同调和循环同调之间的映射，以及其在矩阵代数中同调理论的应用。

Symplectic Reflection Algebras in Positive Characteristic as Ore Extensions

We investigate PBW deformations H of k[x,y]#G where G is the cyclic group of order p and k also has characteristic p; in these deformations, [x,y] takes a value in kG. These algebras are versions of symplectic reflection algebras that only exist in positive characteristic. They also happen to possess a presentation as an Ore extension over a commutative subring R, and via the derivation defining the extension, have interesting connections to certain polynomials appearing in combinatorics and related to alternating permutations (the André polynomials). We find the center of these algebras, thei…

Cyclic A_\infty Structures and Deligne's Conjecture

First we describe a class of homotopy Frobenius algebras via cyclic operads which we call cyclic $A_\infty$ algebras. We then define a suitable new combinatorial operad which acts on the Hochschild cochains of such an algebra in a manner which encodes the homotopy BV structure. Moreover we show that this operad is equivalent to the cellular chains of a certain topological (quasi)-operad of CW complexes whose constituent spaces form a homotopy associative version of the Cacti operad of Voronov. These cellular chains thus constitute a chain model for the framed little disks operad, proving a cyc…