Related papers: Lifting endomorphisms to automorphisms

Nichols algebras are a fundamental building block of pointed Hopf algebras. Part of the classification program of finite-dimensional pointed Hopf algebras with the lifting method of Andruskiewitsch and Schneider is the determination of the…

We prove that the stable endomorphism algebra of a module without self-extensions over a special biserial algebra is a gentle algebra. In particular, it is again special biserial. As a consequence, any algebra which is derived equivalent to…

The eigenvectors of an ergodic semigroup of linear normal positive unital maps on a von Neumann algebra are described. Moreover, it is shown by means of examples, that mere positivity of the maps in question is not sufficient for Frobenius…

Suppose $\mathscr M$ and $\mathscr N$ are von Neumann algebras. Two operators $A$ and $B$ in $\mathscr M$ are said to be orthogonal if $A^*B=0$, meaning their ranges are orthogonal. Let $\varphi\colon\mathscr M\to\mathscr N$ be a map. We…

A digraph is attached to any evolution algebra. This graph leads to some new purely algebraic results on this class of algebras and allows for some new natural proofs of known results. Nilpotency of an evolution algebra will be proved to be…

In the study of pre-Lie algebras, the concept of pre-morphism arises naturally as a generalization of the standard notion of morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative…

In the present paper automorphisms, local and 2-local automorphisms of $n$-dimensional null-filiform and filiform associative algebras are studied. Namely, a common form of the matrix of automorphisms and local automorphisms of these…

A generalization of down-up algebras was introduced by Cassidy and Shelton (J. Algebra 279 (2004), no. 1), the so-called generalized down-up algebras. We describe the automorphism group of conformal Noetherian generalized down-up algebras…

This paper explores various algebraic and homotopical aspects of Nijenhuis Lie conformal algebras, including their cohomology theory, $\mathcal{L}_\infty$-structures, non-abelian extensions, and automorphism groups. We define the cohomology…

The new notion of adjoint algebraic entropy of endomorphisms of Abelian groups is introduced. Various examples and basic properties are provided. It is proved that the adjoint algebraic entropy of an endomorphism equals the algebraic…

We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our…

We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…

Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…

It is known that random 2-lifts of graphs give rise to expander graphs. We present a new conjectured derandomization of this construction based on certain Mealy automata. We verify that these graphs have polylogarithmic diameter, and…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

We consider AF-flows, i.e., one-parameter automorphism groups of a unital simple C*-algebra which leave invariant the dense union of an increasing sequence of finite-dimensional *-subalgebras, and derive two properties for these; an absence…

We describe the groups of inner and outer automorphisms of the free metabelian nilpotent Lie algebra of finite rank over a field of characteristic 0. To obtain this result we first describe the groups of inner and continuous outer…

In this work, we study the concept of self-overlapping permutations, which is related to the larger study of consecutive patterns in permutations. We show that this concept admits a simple and clear geometrical meaning, and prove that a…

We prove constructively the existence of surjective morphisms from affine space onto certain open subvarieties of affine space of the same dimension. For any algebraic set $Z\subset \mathbb{A}^{n-2}\subset \mathbb{A}^{n}$, we construct an…

In this paper, we introduce the concepts of endomorphism operator, left averaging operator, differential operator and Rota-Baxter Operator, and we construct examples of these linear maps on associative algebras with a left identity, a…