Related papers: Duality and modular class of a Nambu-Poisson struc…
After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson…
We establish a canonical isomorphism between two bigraded cohomology theories for polyhedral spaces: Dolbeault cohomology of superforms and tropical cohomology. Furthermore, we prove Poincar\'e duality for cohomology of tropical manifolds,…
We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…
This paper is mainly devoted to a structure study of Hom-alternative algebras . Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are displayed. Moreover some results about Hom-alternative bimodule…
In work the internal structure of de Rham cohomology is considered. As examples the phase flows in $\mathbb {R}^3$ admitting the Nambu Poisson structure are studied.
This paper is a survey (may be incomplete) on partial Nambu-Poisson structures in infinite dimension, mainly in the convenient setting. These ones can be seen as a generalization of both partial Poisson and Nambu-Poisson structures. We also…
This paper offers an adaptation to the convenient setting of finite dimensional Nambu-Poisson structures. In particular, for partial Nambu structures, we look for those whose classical geometrical results in finite dimension can be extended…
We construct Hida and Coleman theories for the degree 0 and 1 cohomology of automorphic line bundles on the modular curve and we define a p-adic duality pairing between the theories in degree 0 and 1.
We study the geometric and algebraic properties of the twisted Poisson structures on Lie algebroids, leading to a definition of their modular class and to an explicit determination of a representative of the modular class, in particular in…
In this paper, we study moduli spaces of representations of certain quivers with relations. For quivers without relations and other categories of homological dimension one, a lot of information is known about the cohomology of their moduli…
We study dualities between classes of relational topological structures, given by Hom-functors. We show that there exists a 2-element structure with infinitely many relations, which reconstructs all other structures generated by a 2-element…
The study of $n$-Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to define cohomology complexes and study…
We review some facts about various T-dualities and sigma models on group manifolds, with particular emphasis on supersymmetry. We point out some of the problems in reconciling Poisson-Lie duality with the bi-hermitean geometry of N=2…
We give explicit examples of degree 3 cohomology classes not Poincare dual to submanifolds, and discuss the realisability of homology classes by submanifolds with Spin-C normal bundles.
We develop a theory of sheaves and cohomology on the category of proper modulus pairs. This complements [KMSY21], where a theory of sheaves and cohomology on the category of non-proper modulus pairs has been developed.
In this paper we study the modular classes of Dirac manifolds and of Dirac maps, and we discuss their basic properties. We apply these results to explain the relationship between the modular classes of the various structures involved in the…
For the Cousin complex of certain modules, we investigate finiteness of cohomology modules, local duality property and injectivity of its terms. The existence of canonical modules of Noetherian non-local rings and the Cousin complexes of…
We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…
In this paper, we study the Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between the Poisson homology and the Poisson cohomology, similar to the duality between the Hochschild…
We compute the Poisson cohomology of the one-parameter family of SU(2)-covariant Poisson structures on the homogeneous space S^{2}=CP^{1}=SU(2)/U(1), where SU(2) is endowed with its standard Poisson--Lie group structure,thus extending the…