Algebraic Geometry over Algebraic Structures. VIII. Geometric Equivalences and Special Classes of Algebraic Structures

Algebraic and geometric structures of Special Relativity

I review, on an advanced level, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie algebra, comparison with the Galilei group, Einstein synchronization, the lattice of causally and chronologically complete regions in Minkows...

Intrinsic computability over algebraic structures

The notion of computable function can be extended from the natural numbers to other domains, using an indexing. Usually, the choice of the indexing affects the set of computable functions and there is no intrinsic notion of computability over these domains. In this paper, we show that, in contrast, when we extend the notion of computable function to algebraic structures, we obtain an intrinsic ...

MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES

By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...

Algebraic and Geometric Structures in String Backgrounds

We give a brief introduction to the study of the algebraic structures – and their geometrical interpretations – which arise in the BRST construction of a conformal string background. Starting from the chiral algebra A of a string background, we consider a number of elementary but universal operations on the chiral algebra. From these operations we deduce a certain fundamental odd Poisson struct...

Algebraic Structures