Endomorphism monoids have long been of interest in universal algebra and also in the study of particular classes of algebraic structures. For any algebra, the set of endomorphisms is closed under composition and forms a monoid (that is, a semigroup with identity). The endomorphism monoid is an interesting structure from a given algebra. In this thesis we study the structure and properties of th...

A subtheory of a quantum eld theory speciies von Neumann subalgebras A(O) (thèob-servables' in the space-time region O) of the von Neumann algebras B(O) (thèèlds ' localized in O). Every local algebra being a (type III 1) factor , the inclusion A (O) B (O) is a sub-factor. The assignment of these local subfactors to the space-time regions is called a ` net of subfactors '. The theory of subfact...

Abstract In supersingular isogeny-based cryptography, the path-finding problem reduces to endomorphism ring problem. Can be reduced knowing just one endomorphism? It is known that a small degree enables polynomial-time and computation (in: Love Boneh, ANTS XIV-Proceedings of Fourteenth Algorithmic Number Theory Symposium, volume 4 Open Book Ser. Math. Sci. Publ., Berkeley, 2020). An gives an ex...

We consider the algebra $\dot\Sigma(\mathcal L)$ generated by inner-limit derivations over ${\rm GICAR}$ of a fermion gas populating an aperiodic Delone set $\mathcal L$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to lattice, we demonstrate that image $\dot \Sigma(\mathcal through Fock representation can be completed gro...