Related papers: Unimodular Hunting II
We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.
Let L and L' be two integral Euclidean lattices in the same genus. We give an asymptotic formula for the number of Kneser p-neighbors of L which are isometric to L', when the prime p goes to infinity. In the case L is unimodular, and if we…
We give an elementary classification and presentation of the finite quaternionic reflection groups of rank two, based on the notion of a``reflection system''. This simplifies the existing classification, which is shown to be incomplete,…
The methods to classify extremal unimodular lattices with given automorphisms are extended to the situation of modular lattices. A slightly more general notion than the type from the PhD thesis of Michael Juergens is the det-type. The…
In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.
In this paper, we construct and classify a class of non-weight modules over the BMS-Kac-Moody algebra, which are free modules of rank one when restricted to the universal enveloping algebra of the Cartan subalgebra (modulo center). We give…
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
It is shown that the coincidence isometries of certain modules in Euclidean $n$-space can be decomposed into a product of at most $n$ coincidence reflections defined by their non-zero elements. This generalizes previous results obtained for…
We show that there are uncountably many countable lattices. We give a discussion of which such lattices can be modular or distributive. The method applies to show that certain other classes of structures also have uncountably many…
A root lattice is a finite rank $\mathbb{Z}$-lattice generated by elements $x$ satisfying $x\cdot x=2$. It is well-known that the root lattices have an $ADE$ classification and they play a prominent role in the study of even unimodular…
We collect a number of striking recent results in a study of dimers on infinite regular bipartite lattices and also on regular bipartite graphs. We clearly separate rigorously proven results from conjectures. A primary goal is to show…
We study the category M consisting of U(sl_{n+1})-modules whose restriction to U(h) is free of rank 1, in particular we classify isomorphism classes of objects in M and determine their submodule structure. This leads to new…
In this paper we study indecomposable rank 2 modules in the Grassmannian cluster category ${\rm CM}(B_{5,10})$. This is the smallest wild case containing modules whose profile layers are $5$-interlacing. We construct all rank 2…
In this note, we summarize known results and open questions on the existence of isometric embeddings between different Schatten classes as well as obtain a new non-embeddability result using a novel method. We also provide a brief overview…
We study two categories of ${U}(\mathfrak h)$-free $\mathfrak{sl}(m|n)$-modules of total rank 2: $\mathcal{M}_{\mathfrak{sl}(m|n)}(2)$, whose objects are free of rank 2 over ${U}(\mathfrak h)$ which are not necessarily $\mathbb Z_2$-graded,…
We present an algorithm to enumerate isometry classes of integral quadratic lattices of a given rank and determinant, and analyze its running time by giving bounds on the number of genus symbols for a fixed rank and determinant. We build on…
This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras…
Using the Galatius--Kupers--Randal-Williams framework of cellular $E_2$-algebras, we prove a secondary stability theorem for mapping class groups of nonorientable surfaces. As a corollary, we obtain a new best known stability range for the…
It is a well-known result of Etingof, Nikshych and Ostrik that there are finitely many inequivalent integral modular categories of any fixed rank $n$. This follows from a double-exponential bound on the maximal denominator in an Egyptian…
We give necessary and sufficient conditions for an integral polynomial without linear factors to be the characteristic polynomial of an isometry of some even, unimodular lattice of given signature. This gives rise to Hasse principle…