Related papers: One Lie group to define them all
In this note we envisage the relation existing between the Lie Groups and the Theory of Complex Variables. In particular, it is shown that the dimensions of the irreducibles representations of $SU(N)$ may be written in terms of the…
We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…
We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…
A Lie group is a group that is also a differentiable manifold, such that the group operation is continuous respect to the topological structure. To every Lie group we can associate its tangent space in the identity point as a vector space,…
By means of a generalization of the S-expansion method we construct a procedure to obtain expanded higher-order Lie algebras. It is shown that the direct product between an Abelian semigroup S and a higher-order Lie algebra…
A Lie system is a system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields: a so-called Vessiot-Guldberg Lie…
We call a finite, spanning set of a semi-simple real Lie algebra a distinguished set if it satisfies the following property: The Lie bracket of any two elements out of the set is, up to some constant, another element in the set; conversely,…
In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.
We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.
In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces of suitable Lie groups. Using the formalism of Lie groups and…
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…
We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
We prove several basic extension theorems for reductive group schemes. We also prove that each Lie algebra with a perfect Killing form over a commutative $\dbZ$-algebra, is the Lie algebra of an adjoint group scheme.
A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more…
A multiplicatively closed, horizontal foliation on a Lie groupoid may be viewed as a "pseudoaction" on the base manifold $M$. A pseudoaction generates a pseudogroup of transformations of $M$ in the same way an ordinary Lie group action…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
Two Lie algebroids are presented that are linked to the construction of the linearizing output of an affine in the input nonlinear system. The algorithmic construction of the linearizing output proceeds inductively, and each stage has two…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.