Related papers: A note on construction of the Leech lattice
Skew lattices are non-commutative generalizations of lattices, and the cosets represent the building blocks that skew lattices are built of. As by Leech's Second Decomposition Theorem any skew lattice embeds into a direct product of a…
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.
In a recent paper, G. Cz\'edli and E.\,T. Schmidt present a structure theorem for planar semimodular lattices. In this note, we present an alternative proof.
In the paper [V. Adler, IMRN {\bf 1} (1998) 1--4] a lattice version of the Krichever-Novikov equation was constructed. We present in this note its Lax pair and discuss its elliptic form.
I briefly introduce the methods by which lattice QCD predictions for RHIC are obtained. Next I deal with lattice determinations of strangeness production and event-to-event fluctuations of conserved quantities. I also present a new…
We introduce the free Banach lattice generated by a lattice L. We give an explicit description of it and we study some of its properties for the case when $\mathbb{L}$ is a linear order, like the countable chain condition.
The aim of this paper is to give a simple construction of the free skew-brace over a set $X$.
The Leech lattice, $\Lambda_{24}$, is represented on the space of octonionic 3-vectors. It is built from two octonionic representations of $E_{8}$, and is reached via $\Lambda_{16}$. It is invariant under the octonion index cycling and…
The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.
We describe the construction of the slice fibration of a given one.
This note presents an interesting counterexample to a basic covering problem.
In this talk I briefly comment on the conventional lattice gauge fixing adopting a critical, even though constructive, numerical point of view.
We propose a construction of lattices from (skew-) polynomial codes, by endowing quotients of some ideals in both number fields and cyclic algebras with a suitable trace form. We give criteria for unimodularity. This yields integral and…
The present note sketches a theory of constructs.
An elementary approach to the construction of Coxeter group representations is presented.
We restate a process presented by Stanley as a technique to prove that there exists exactly one $d$-differential distributive lattice for any positive integer $d$. This process can be trivially extended to apply to distributive finitary…
In this paper, we show that there is a frame of norm k in the odd Leech lattice for every k\ge 3.
We review the method developed in Pisa to determine the topological susceptibility in lattice QCD and present a collection of new and old results obtained by the method.
We construct a nonuniform lattice and an infinite family of uniform lattices in the automorphism group of a hyperbolic building with all links a fixed finite building of rank 2 associated to a Chevalley group. We use complexes of groups and…
We introduce the notion of a building lattice generalizing tree lattices. We give a Lefschetz formula and apply it to geometric zeta functions. We further generalize Bass's approach to Ihara zeta functions to the higher dimensional case of…