Related papers: Insertion and Lie Bracket Concerning Finite Sets
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
We introduce the problem of partitioning 2D regions (usually convex regions) into mutually congruent pieces ('tiles').
We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets $\{H,\phi_i\}$ and $\{\phi_i,\phi_j\}$, where $H$ is the Hamiltonian and $\phi_i$ are primary and secondary…
This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor…
A Cartan Calculus of Lie derivatives, differential forms, and inner derivations, based on an undeformed Cartan identity, is constructed. We attempt a classification of various types of quantum Lie algebras and present a fairly general…
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion…
We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference "Noncommutative geometry and applications," Frascati, Italy, June 16-21, 2014.…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
A general construction of an sh Lie algebra from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines…
Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
Using the combinatorial species setting, we propose two new operad structures on multigraphs and on pointed oriented multigraphs. The former can be considered as a canonical operad on multigraphs, directly generalizing the…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
Given a nonempty set $\mathcal{L}$ of linear orders, we say that the linear order $L$ is $\mathcal{L}$-convex embeddable into the linear order $L'$ if it is possible to partition $L$ into convex sets indexed by some element of $\mathcal{L}$…
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…
This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising…
We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category…