Related papers: Conference matrices and unimodular lattices
Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\leq 4$. We identify such a class by employing…
Schur decompositions and the corresponding Schur forms of a single matrix, a pair of matrices, or a collection of matrices associated with the periodic eigenvalue problem are frequently used and studied. These forms are upper-triangular…
Inspired by the work of Izakhian and Rhodes, a theory of representation of hereditary collections by boolean matrices is developed. This corresponds to representation by finite $\vee$-generated lattices. The lattice of flats, defined for…
We determine the contact mapping class group of the standard contact structures on lens spaces. To prove the main result, we use the one-parametric convex surface theory to classify Legendrian and transverse rational unknots in any tight…
A class of Cantor-type spaces and related geometric structures are discussed.
Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra…
Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define…
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique…
We develop a new form of patching that is both far-reaching and more elementary than the previous versions that have been used in inverse Galois theory for function fields of curves. A key point of our approach is to work with fields and…
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…
Embeddings of word structures into matrix semigroups provide a natural bridge between combinatorics on words and linear algebra. However, low-dimensional matrix semigroups impose strong structural restrictions on possible embeddings.…
We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…
In this paper, we consider the versal deformations of three dimensional Lie algebras. We classify Lie algebras and study their deformations by using linear algebra techniques to study the cohomology. We will focus on how the deformations…
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices $L$ whose Gram matrix contains only non-negative…
We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: (a) groups of germs…
We discuss various old and new definitions of the notion of a vector field on a convenient manifold that can be proved to give rise to Lie algebras, and are in finite dimensions equivalent to the standard notion of a vector field.
A new characterization is provided for the class of compact rank-one symmetric spaces. Such spaces are the only symmetric spaces of compact type for which the standard vector field on their sphere bundles is Killing with respect to some…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…