Related papers: A note on a homological epimorphism whose source i…

In this short note, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by L.…

A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an…

We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair…

Given any $f$ a locally finitely piecewise affine homeomorphism of $\Omega \subset \mathbb{R}^d$ onto $\Delta \subset \mathbb{R}^d$ (for $d=3, 4$) such that $f\in W^{1,p}(\Omega, \mathbb{R}^d)$ and $f^{-1}\in W^{1,q}(\Delta, \mathbb{R}^d)$,…

We prove existence results for Dirac-harmonic maps using index theoretical tools. They are mainly interesting if the source manifold has dimension 1 or 2 modulo 8. Our solutions are uncoupled in the sense that the underlying map between the…

Let $A=\oplus_{i\in \mathbb{Z}}A_i$ be a finite dimensional graded symmetric cellular algebra with a homogeneous symmetrizing trace of degree $d$. We prove that $A_{-d}$ contains the Higman ideal $H(A)$ of the center of $A$ and $\dim…

Let $k$ be a field of characteristic not two or three. We classify up to isomorphism all finite-dimensional Lie superalgebras $\mathfrak{g}=\mathfrak{g}_0\oplus \mathfrak{g}_1$ over $k$, where $\mathfrak{g}_0$ is a three-dimensional simple…

Let $R$ be a semilocal Dedekind domain with fraction field $F$. We show that two hereditary $R$-orders in central simple $F$-algebras which become isomorphic after tensoring with $F$ and with some faithfully flat \'etale $R$-algebra are…

In this paper, we consider compatible Hom-associative algebras as a twisted version of compatible associative algebras. Compatible Hom-associative algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie…

Let $R$ be a commutative noetherian ring and $f: X \to \mathrm{Spec} R$ a proper smooth morphism, of relative dimension $n$. From Hartshorne, Residues and Duality, Springer, 1966, one knows that the trace map $\mathrm{Tr}_f :…

Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that…

We study a class of chainable continua which contains, among others, all inverse limit spaces generated by a single interval bonding map which is piecewise monotone and locally eventually onto. Such spaces are realized as attractors of…

Let f be a class P -homeomorphism of the circle. We prove that there exists a piecewise analytic homeomorphism that conjugate f to a one-class P with prescribed break points lying on pairwise distinct orbits. As a consequence, we give a…

We study harmonic morphisms of graphs as a natural discrete analogue of holomorphic maps between Riemann surfaces. We formulate a graph-theoretic analogue of the classical Riemann-Hurwitz formula, study the functorial maps on Jacobians and…

The aim of this work is to study a kind of refinement of the entropy conjecture, in the context of partially hyperbolic diffeomorphisms with one dimensional central direction, of d-dimensional torus. We start by establishing a connection…

In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…

Hereditary algebras are quasi-hereditary with respect to any adapted partial order on the indexing set of the isomorphism classes of their simple modules. For any adapted partial order on $\{1,\dots, n\}$, we compute the quiver and…

There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the…

We prove that among the finite dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the property that the middle term of an arbitrary extension of indecomposable modules has at…

Let $\mathfrak{g}$ be a finite-dimensional complex Lie algebra and $\textrm{HLie}_{m}(\mathfrak{g})$ be the affine variety of all multiplicative Hom-Lie algebras on $\mathfrak{g}$. We use a method of computational ideal theory to describe…