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We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and…
Motivated by reconstruction results by Rubin, we introduce a new reconstruction notion for permutation groups, transformation monoids and clones, called automatic action compatibility, which entails automatic homeomorphicity. We further…
We present a simple extension of the classical Hilton-Eckmann argument classically used to prove that the endomorphism monoid of the unit object in a monoidal category is commutative. It allows us to recover in a uniform way well-known…
We introduce the notion of generalized hyperpolygon, which arises as a representation, in the sense of Nakajima, of a comet-shaped quiver. We identify these representations with rigid geometric figures, namely pairs of polygons: one in the…
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…
The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…
Given any pair of positive integers m and n, we construct a new Hopf algebra, which may be regarded as a degenerate version of the quantum group of gl(m+n). We study its structure and develop a highest weight representation theory. The…
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure via the representation theory of families of algebras. This…
It is well-known that small categories have equivalent descriptions as partial monoids. We provide a formulation of partial monoid and partial monoid homomorphism involving $s$ and $t$ instead of identities and then following a recent…
In this paper, we provide a comprehensive classification of Stein's groups, which generalize the well-known Higman-Thompson groups. Stein's groups are defined as groups of piecewise linear bijections of an interval with finitely many…
Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven. It is shown that these biequivalences categorify results in…
Magnetic vortices and skyrmions are typically characterized by distinct topological invariants. This work presents a unified approach for the topological classification of these textures, encompassing isolated objects and configurations…
In this paper, we study invariant Poisson structures on homogeneous manifolds, which serve as a natural generalization of homogeneous symplectic manifolds previously explored in the literature. Our work begins by providing an algebraic…
We prove that any invariant hypercomplex structure on a homogeneous space $M = G/L$ where $G$ is a compact Lie group is obtained via the Joyce's construction, provided that there exists a hyper-Hermitian naturally reductive invariant metric…
We prove refined generating series formulae for characters of (virtual) cohomology representations of external products of suitable coefficients, e.g., (complexes of) constructible or coherent sheaves, or (complexes of) mixed Hodge modules…
We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…
We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked points, we consider the moduli of generalized complex structures…
Let $A$ be a separable $C^*$-algebra and $B$ a stable $C^*$-algebra containing a strictly positive element. We show that the group $\Ext(SA,B)$ of unitary equivalence classes of extensions of $SA$ by $B$, modulo the extensions which are…
In order to solve two problems in deformation theory, we establish natural structures of homotopy Lie algebras and of homotopy associative algebras on tensor products of algebras of different types and on mapping spaces between coalgebras…
The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…