Related papers: Statistical Geometry and Hessian Structures on Pre…

We generalize cubic norm structures to cubic norm pairs and extend hermitian cubic norm structures to arbitrary commutative unital rings. For the associated ``skew dimension one structurable algebra" of these pairs, we construct a…

Let $M$ be a compact oriented $3$-manifold with boundary consisting of tori, and let $G$ be a semisimple algebraic group. We define the adjoint torsion function on the moduli stack of $G$-local systems on $M$ satisfying a certain regularity…

This thesis studies the representation theory and linear structures of $\mathcal{Q}$-manifolds and higher Lie algebroids. We introduce differential graded modules (or for short DG-modules) of $\mathcal{Q}$-manifolds and the equivalent…

Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a…

A Koszul-Vinberg manifold is a generalization of a Hessian manifold, and their relation is similar to the relation between Poisson manifolds and symplectic manifolds. Koszul-Vinberg structures and Poisson structures on manifolds extend to…

Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…

We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…

In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E^*, where E -> M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even…

We define the notion of hom-Batalin-Vilkovisky algebras and strong differential hom-Gerstenhaber algebras as a special class of hom-Gerstenhaber algebras and provide canonical examples associated to some well-known hom-structures.…

The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…

We show that the pair given by the power set and by the "Grassmannian"(set of all subgroups) of an arbitrary group behaves very much like the pair given by a projective space and its dual projective space. More precisely, we generalize…

We extend the notion of Lie bialgebroids for more general bracket structures used in string and M theories. We formalize the notions of calculus and dual calculi on algebroids. We achieve this by reinterpreting the main results of the…

Let G be the group of all formal power series starting with x with coefficients in a field k of zero characteristic (with the composition product), and let F[G] be its function algebra. C. Brouder and A. Frabetti introduced a…

This is a survey of our research on geometric structures of projective embeddings and includes some topics of our talks in several symposia during 1990-99. We clarify our main problem, which is to construct a kind of geometric composition…

We develop a mathematical concept towards gauge field theories based upon a Hilbert space endowed with a representation of a skew-adjoint Lie algebra and an action of a generalized Dirac operator. This concept shares common features with…

The class of statistical manifolds with divisible cubic forms arises from affine differential geometry. We examine the geodesic connectedness of affine connections on this class of statistical manifolds. In information geometry, the…

We develop a Heisenberg-picture \emph{kinematical} framework in which (i) time is treated as a quantum observable, admitting both a relational POVM construction for semibounded spectra and a fully self-adjoint realization on an enlarged…

We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over a commutative semiring S. In particular, we obtain a complete characterization of congruence-simpleness for such Steinberg algebras, extending the…

The theory of abstract kernels in non-trivial extensions for many kinds of algebraical objects, such as groups, rings and graded rings, associative algebras, Lie algebras, restricted Lie algebras, DG-algebras and DG-Lie algebras, has been…

We compare the notions of metric-compatibility and torsion of a connection in the frameworks of Beggs-Majid and Mesland-Rennie. It follows that for $\ast$-preserving connections, compatibility with a real metric in the sense of Beggs-Majid…