Related papers: Rank 2 fusion rings are complete intersections
For any normal commutative Hopf subalgebra $K=k^G$ of a semisimple Hopf algebra we describe the ring inside $kG$ obtained by the restriction of $H$-modules. If $G=\Z_p$ this ring determines a fusion ring and we give a complete description…
Let $\C$ be a self-dual fusion category of rank $4$ which has a nontrivial proper fusion subcategory. We identify three new families of Grothendieck rings for $\C$: one of them is completely determined, the other two are parameterized by…
We consider string junctions with endpoints on a set of branes of IIB string theory defining an ADE-type gauge Lie algebra. We show how to characterize uniquely equivalence classes of junctions related by string/brane crossing through…
A ringoid is a set with two binary operations that are linked by the distributive laws. We study special classes of ringoids that are congruence-simple or ideal-simple. In particular, we examine generalised parasemifields and…
A nef-partition for a weighted complete intersection is a combinatorial structure on its weights and degrees which is important for Mirror Symmetry. It is known that nef-partitions exist for smooth well-formed Fano weighted complete…
We consider varieties generated by finite closure algebras whose canonical relations have two levels, and whose restriction to a level is an "extremal" relation, i.e. the identity or the universal relation. The corresponding logics have…
We construct and study various dual pairs between finite dimensional classical Lie groups and infinite dimensional Lie algebras in some Fock representations. The infinite dimensional Lie algebras here can be either a completed infinite rank…
The aim of this work is to determine the quasi-filiform Lie algebras that are completable. We further prove that for any positive integer $m$ there exists a complete Lie algebra, the second cohomology group of which has dimension greater or…
Associating to each pre-order on the indices 1,...,n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n x n matrix rings. Rings within the order-convex hull of…
The aim of this work is to prove the nonexistence of complex structures over nilpotent Lie algebras of maximal class (also called filiform).
In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtained illustrate a significant difference between the classes…
We provide a detailed analysis of atomic *-representations of rank 2 graphs on a single vertex. They are completely classified up to unitary equivalence, and decomposed into a direct sum or direct integral of irreducible atomic…
We prove that Bi-Zassenhaus loop algebras are finitely presented up to central and second central elements. In particular, we show an explicit finite presentation for a Lie algebra whose quotient over its second centre is isomorphic to a…
Let $A$ be an associative algebra over a field of characteristic $\neq 2$ that is generated by a finite collection of nilpotent elements. We prove that all Lie derived powers of $A$ are finitely generated Lie algebras.
The fusion rings associated to affine Kac-Moody algebras appear in several different contexts in math and mathematical physics. In this paper we find all automorphisms of all affine fusion rings, or equivalently the symmetries of the…
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…
The fusion rules and modular matrix of a rational conformal field theory obey a list of properties. We use these properties to classify rational conformal field theories with not more than six primary fields and small values of the fusion…
We introduce a complete radical formula for modules over non-commutative rings which is the equivalence of a radical formula in the setting of modules defined over commutative rings. This gives a general frame work through which known…
We prove that any quadratic complete intersection with certain action of the symmetric group has the strong Lefschetz property over a field of characteristic zero. As a consequence of it we construct a new class of homogeneous complete…
In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.