Related papers: Abelian Complex Structures and Generalizations
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids and construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an E-Courant…
The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and…
Basing ourselves on Janelidze and Kelly's general notion of central extension, we study universal central extensions in the context of semi-abelian categories. Thus we unify classical, recent and new results in one conceptual framework. The…
We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.
The Poisson structure arising in the Hamiltonian approach to the rational Gaudin model looks very similar to the so-called modified Reflection Equation Algebra. Motivated by this analogy, we realize a braiding of the mentioned Poisson…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…
ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).
We give an algebraic description of the structure of the analytic universal cover of a complex abelian variety which suffices to determine the structure up to isomorphism. More generally, we classify the models of theories of "universal…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…
In this paper, two parallel notions of convexity of sets are introduced in the abelian semigroup setting. The connection of these notions to algebraic and to set-theoretic operations is investigated. A formula for the computation of the…
We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle $E\to…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
In this work we present some arithmetic properties of families of abelian $p$--extensions of global function fields, among which are their generators and their type of ramification and decomposition.
We study left-invariant generalized K\"ahler structures on almost abelian Lie groups, i.e., on solvable Lie groups with a codimension-one abelian normal subgroup. In particular, we classify six-dimensional almost abelian Lie groups which…
We study rack and quandle coverings from a universal algebraic viewpoint and we show how they can be understood using the notion of strongly abelian congruences. We provide an abstract characterization of several particular types of…
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…