In the structure theory of quantized enveloping algebras, the algebra isomorphisms determined by Lusztig led to the first general construction of PBW bases of these algebras. Also, they have important applications to the representation theory of these and related algebras. In the present paper the Drinfel’d double for a class of graded Hopf algebras is investigated. Various quantum algebras, in...

We find and describe unexpected isomorphisms between two very different objects associated to hypersurface singularities. One object is the Milnor algebra of a function, while the other object associated to a singularity is the local ring of the flatness stratum of the singular locus in a miniversal deformation, an invariant of the contact class of a defining function. Such isomorphisms exist f...

Curry-style system F, i.e. system F with no explicit types in terms, can be seen as a core presentation of polymorphism from the point of view of programming languages. This paper gives a characterisation of type isomorphisms for this language, by using a game model whose intuition comes both from the syntax and fromthe game semantics universe. Themodel is composed of: an untyped part to interp...

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.

The classical Loewner’s theorem states that operator monotone functions on real intervals are described by holomorphic the upper half-plane. We characterize local order isomorphisms domains biholomorphic automorphisms of generalized half-plane, which is collection all operators with positive invertible imaginary part. describe such maps in an explicit manner, and examine properties maximal isom...

Landau-Ginzburg mirror symmetry studies isomorphisms between Aand B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial W and a related symmetry group G. Given two polynomials W1, W2 with the same weights and same group G, the corresponding A-models built with (W1,G) and (W2,G) are isomorphic. Though the same result cannot hold in full genera...

In this paper we propose a multiplicative blinding scheme for protecting implementations of a scalar multiplication over elliptic curves. Specifically, this blinding method applies to elliptic curves in the short Weierstraß form over large prime fields. The described countermeasure is shown to be a generalization of the use of random curve isomorphisms to prevent side-channel analysis, and our ...

On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the Knizhnik--Zamolodchikov connection and have finite order. When all primary fields are fixed points, the isomorphisms are endomorphisms; in this case, the bund...

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.