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The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence,…

This paper investigates conditions under which a given automorphism of a residually torsion-free nilpotent group respects some ordering of the group. For free groups and surface groups, this has relevance to ordering the fundamental groups…

The notion of associativity (which differs from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for operations of high arity is introduced. It is proved that the…

This paper is devoted to a study of the automorphism groups of three series of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over a field of prime characteristic. Our aim is to characterize the connections between…

Association schemes on triples (ASTs) are ternary analogues of classical association schemes, whose relations and adjacency algebras are ternary instead of binary. We provide a survey of the current progress in the study of ASTs,…

In this paper, we establish a precise connection between higher rho invariants and delocalized eta invariants. Given an element in a discrete group, if its conjugacy class has polynomial growth, then there is a natural trace map on the…

The so-called Tits class, associated to an adjoint absolutely almost simple algebraic group, provides a cohomological obstruction for this group to admit an outer automorphism. If the group has inner type, this obstruction is the only one.…

We associate an square to any two dimensional evolution algebra. This geometric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the identities of degrees…

In this paper, we investigate subnormal subgroups of the multiplicative group of an almost locally simple artinian algebra with involution. In particular, we show that if either the set of traces or the set of norms of such a subgroup with…

For a function algebra A we investigate relations between the following three topics: isomorphisms of singly generated A-modules, Morita equivalence bimodules, and `real harmonic functions' with respect to A. We also consider certain groups…

We study the mapping class group of a nontrivial irreducible shift of finite type: the group of flow equivalences of its mapping torus modulo isotopy. This group plays for flow equivalence the role that the automorphism group plays for…

This paper is devoted to study local automorphisms of $p$-filiform Leibniz algebras. We prove that $p$-filiform Leibniz algebras as a rule admit local automorphisms which are not automorphisms.

These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.

We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is naturally isomorphic to the second lazy cohomology group of…

We construct families of birational involutions on $\mathbb{P}^3$ or a smooth cubic threefold which do not fit into a non-trivial elementary relation of Sarkisov links. As a consequence, we construct new homomorphisms from their group of…

For all algebraic groups over non-Archimedean local fields, the bounded cohomology vanishes. This follows from the corresponding statement for automorphism groups of Bruhat--Tits buildings, which hinges on the solution to the flatmate…

Any non-abelian finite $p$-group has a non-inner automorphism of order $p$.

Let $1 \to N \to G \to H \to 1$ be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of $N$ and lifting automorphisms of $H$ to certain automorphisms of $G$.

The present paper is devoted to genetic Volterra algebras. We first study characters of such algebras. We fully describe associative genetic Volterra algebras, in this case all derivations are trivial. In general setting, i.e. when the…

We introduce a non-autonomous generalization of spatial-temporal differentiations, and prove results about probabilistically and topologically generic behaviors of certain spatial-temporal differentiations generated by endomorphisms of…