Related papers: Descent with algebraic structures for symplectic c…

We review how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions.

We classify 0-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf…

This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.

We consider circle patterns on surfaces with complex projective structures. We investigate two symplectic forms pulled back to the deformation space of circle patterns. The first one is Goldman's symplectic form on the space of complex…

We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not…

The aim of this paper is to extend Gerstenhaber formal deformations of algebras to the case of Hom-Alternative and Hom-Malcev algebras. We construct deformation cohomology groups in low dimensions. Using a composition construction, we give…

The B-side of Kontsevich's Homological Mirror Symmetry Conjecture is discussed. We give first a self-contained study of derived categories and their homological algebra, and later restrict to the bounded derived category of schemes and…

Dendriform coalgebras are the dual notion of dendriform algebras and are splitting of associative coalgebras. In this paper, we define a cohomology theory for dendriform coalgebras based on some combinatorial maps. We show that the…

Generalized complex geometry was classically formulated by the language of differential geometry. In this paper, we reformulated a generalized complex manifold as a holomorphic symplectic differentiable formal stack in a homotopical sense.…

We introduce the notion of integrable connections for a sheaf of differential graded algebras on a topological space. We then describe them in the finite locally projective setting, when the sheaf is either the de Rham complex of a formal…

In this work we introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both…

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…

We introduce the notion of cosymplectic structure on Jacobi-Jordan algebras, and we state that they are related to symplectic Jacobi-Jordan algebras. We show, in particular, that they support a right-skew-symmetric product. We also study…

We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…

We define cyclic cohomology of corings over not necessarily commutative algebras. We observe that the key fact which allows us to define this complex is that enveloping algebra of an algebra is a para Hopf algebroid. This observation…

A taming symplectic structure provides an upper bound on the area of an approximately pseudoholomorphic curve in terms of its homology class. We prove that, conversely, an almost complex manifold with such an area bound admits a taming…

Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…

We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in complex geometry. These operators map primitive forms into…

We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in positive characteristic, as well as about log smooth…