Related papers: Linear algebra and group theory

We propose a generalization of the factorization method to the case when $\mathcal{G}$ is a finite dimensional Lie algebra such that $\mathcal{G}=\mathcal{G}_0\oplus M \oplus N$ (direct sum of vector spaces), where $\mathcal{G}_0$ is a…

We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application,…

The notion of a \emph{$G$-completely reducible} subgroup is important in the study of algebraic groups and their subgroup structure. It generalizes the usual idea of complete reducibility from representation theory: a subgroup $H$ of a…

Let V be a finite dimensional complex superspace and G a simple (or a ``close'' to simple) Lie superalgebra of matrix type, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theory for G we mean the description of…

We introduce a generalisation of norm relations in the group algebra Q[G], where G is a finite group. We give some properties of these relations, and use them to obtain relations between the S-unit groups of different subfields of the same…

This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…

We develop a new general framework for algebras and clones, called Universal Clone Algebra. Algebras and clones of finitary operations are to Universal Algebra what t-algebras and clone algebras are to Universal Clone Algebra. Clone…

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category…

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…

We present an operator algebraic approach to Wigner's unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove a generalization of this celebrated theorem for Hilbert…

This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.

We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra $\gl_n$ into $\gl_n\oplus\gl_n$. Its representation theory is related to the theory of decompositions of tensor…

The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…

Let $R$ be the polydisc algebra or the Wiener algebra. It is shown that the group $SL_n(R)$ is generated by the subgroup of elementary matrices with all diagonal entries $1$ and at most one nonzero off-diagonal entry. The result an easy…

We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of…

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. Actually, the observations show there are two resources to get classification of filiform Leibniz algebras. The first of them…

In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems…

By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…

Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…

This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of…