Amalgamated graph transformation allows to define schemes of rules coinciding in common core activities and differing over additional parallel independent activities. Consequently, a rule scheme is specified by a kernel rule and a set of extending multi-rules forming an interaction scheme. Amalgamated transformations have been increasingly used in various modeling contexts. Critical Pair Analys...

‎The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B ‎and a subgroup $H$ of $Gamma$ induces‎, ‎under general conditions‎, ‎a ‎group-like structure for B‎, ‎known as a gyrogroup‎. ‎The famous‎ concrete realization of a gyrogroup‎, ‎which motivated the emergence ‎of gyrogroups into the mainstream‎, ‎is the space of all ‎relativistically admissible velocities along with a binary ‎mbox{...

In Ufnarovski (1989), the concept of automaton algebras is introduced. These are quotients of the non-commutative polynomial ring where the defining ideal allows some Gröbner basis with a regular set of leading words. However, nothing is reflected concerning the whole structure of the Gröbner basis (except of course for monomial algebras). In this paper we introduce the concept of regular Gröbn...

The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite root system considered. Although the irreducible modules obtained in this way are not of highest weight, they admit a crystal basis and a canonical basis. This permits in particular to obtain for each familly of classic...

Bialgebras and their specialisation Hopf algebras are algebraic structures that challenge traditional mathematical notation, in that they sport two core operations that defy the basic functional paradigm of taking zero or more operands as input and producing one result as output. On the other hand, these peculiarities do not prevent studying them using rewriting techniques, if one works within ...

We investigate doubled (generalized) complex structures in $2D$-dimensional Born geometries where T-duality symmetry is manifestly realized. show that K\"{a}hler, hyperk\"{a}hler, bi-hermitian and bi-hypercomplex of spacetime are implemented as structures. find the generalized K\"{a}hler (hyperk\"{a}hler) appear subalgebras bi-quaternions split-tetra-quaternions. parts these classified by Cliff...

In several classes of countable structures it is known that every hyperarithmetic structure has a computable presentation up to bi-embeddability. this article we investigate the complexity embeddings between bi-embeddable in two such classes, linear orders and Boolean algebras. We show if $\mathcal L$ order Hausdorff rank $n$, then for copy there an embedding $2n-1$ jumps from atomic diagrams. ...