相关论文: Modular classes of Poisson-Nijenhuis Lie algebroid…

We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…

We study the ``twisted" Poincar\'e duality of smooth Poisson manifolds, and show that, if the modular vector field is diagonalizable, then there is a mixed complex associated to the Poisson complex, which, combining with the twisted…

We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…

The Lie-Rinehart algebra of a manifold M, defined by the Lie structure of the vector fields, their action and their module structure on the infinitely differentiable functions on M, is a common, diffeomorphism invariant, algebra for both…

The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal…

We study noncommutative generalizations of such notions of the classical symplectic geometry as degenerate Poisson structure, Poisson submanifold and quotient manifold, symplectic foliation and symplectic leaf for associative Poisson…

In this paper we classify indecomposable modules for the Lie algebra of vector fields on a torus that admit a compatible action of the algebra of functions. An important family of such modules is given by spaces of jets of tensor fields.

A double Poisson bracket, in the sense of M. Van den Bergh, is an operation on an associative algebra $A$ which induces a Poisson bracket on each representation space $\operatorname{Rep}(A,n)$ in an explicit way. In this note, we study the…

For any graded bialgebras $A$ and $B$, we define a commutative graded algebra $A_B$ representing the functor of $B$-representations of $A$. When $A$ is a cocommutative graded Hopf algebra and $B$ is a commutative ungraded Hopf algebra, we…

We construct classes of von Neumann algebra modules by considering ``column sums" of noncommutative L^p spaces. Our abstract characterization is based on an L^{p/2}-valued inner product, thereby generalizing Hilbert C*-modules and…

Let $\mathcal{O}$ be a complete discrete valuation ring, $\mathcal{K}$ its quotient field, and $A$ the symmetric Kronecker algebra over $\mathcal{O}$. We consider the full subcategory of the category of $A$-lattices whose objects are…

Non-degenerate bilinear forms over fields of characteristic 2, in particular, non-symmetric ones, are classified with respect to various equivalences, and the Lie algebras preserving them are described. Although it is known that there are…

A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are defined by a decomposable 3-vector field. The key point is the proof of a lemma which tells…

It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…

We discuss the theory of Poisson vertex algebras and their generalizations in relation to integrability of Hamiltonian PDE. In particular, we discuss the theory of affine classical W-algebras and apply it to construct a large class of…

We consider a category of modules that admit compatible actions of the commutative algebra of Laurent polynomials and the Lie algebra of divergence zero vector fields on a torus and have a weight decomposition with finite dimensional weight…

On a Poisson manifold endowed with a Riemannian metric we will construct a vector field that generalizes the double bracket vector field defined on semi-simple Lie algebras. On a regular symplectic leaf we will construct a generalization of…

We introduce three non-compact moduli stacks parametrizing noncommutative deformations of Hirzebruch surfaces; the first is the moduli stack of locally free sheaf bimodules of rank 2, which appears in the definition of noncommutative…

In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny…

In this paper, we investigate the existence of an elementary abelian closure in characteristic not $2$ for biquadratic extensions. We discover that it exists for any non-cyclic extension. We make use of it to obtain a classification for…