Related papers: Elements of Group Theory
In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
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.
Here is a list of chapters: 1 Introduction 2 Notation and preliminaries Part I: Finite quantum groups 3 2x2 Matrix quantum groups and the quantum plane 4 Quantum enveloping algebras at a root of unity Part II: q-Oscillators 5…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
By a global approach, we prove the arithmetic fundamental lemma conjecture for unitary groups in $n$ variables over $\mathbb{Q}_p$ when $p\geq n$.
These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples.…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential geometry on Lie groups 3. Lie algebra…
A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where…
These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and geometric representation theory. They are based on the…
We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…
We deduce a simple representation and the invariant factor decompositions of the subgroups of the group $\Bbb{Z}_m \times \Bbb{Z}_n$, where $m$ and $n$ are arbitrary positive integers. We obtain formulas for the total number of subgroups…
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
A general theoretical framework based on group-subgroup and group-supergroup relations is proposed to describe and to derive interpenetrating nets.
This is a survey. The main subject of this survey is the homotopical or homological nature of certain structures which appear in classical problems about groups, Lie rings and group rings. It is well known that the (generalized) dimension…
There are exactly three finite subgroups of SU(2) that act irreducibly in the spin 1 representation, namely the binary tetrahedral, binary octahedral and binary icosahedral groups. In previous papers I have shown how the binary tetrahedral…