We introduce the notion of multiplicities for an object M in a semi-simple rigid tensor category A, as a collection of central scalars which relate the categorical trace with the ring-theoretic trace. Multiplicities turn out to be rational integers in important cases, most notably when A is of " homological origin ". We show that this integrality condition has simple consequences, like the rati...

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...

As usual, we write Z,Q,Fp,C for the ring of integers, the field of rational numbers, the finite field with p elements and the field of complex numbers respectively. If Z is a smooth algebraic variety over an algebraically closed field then we write Ω(Z) for the space of differentials of the first kind on Z. If Z is an abelian variety then we write End(Z) for its ring of (absolute) endomorphisms...