Related papers: Representation Theory of Polyadic Groups
In this note, we adapt the procedure of the Long-Moody procedure to construct linear representations of welded braid groups. We exhibit the natural setting in this context and compute the first examples of representations we obtain thanks…
The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear…
Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is…
We study the representation theory of three towers of algebras which are related to the symmetric groups and their Hecke algebras. The first one is constructed as the algebras generated simultaneously by the elementary transpositions and…
With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of $Q$-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
Motivated by appearance of multisemigroups in the study of additive $2$-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be better suitable for applications in higher…
We investigate the rate of growth of the function of n which counts the number of complex irreducible representations of a fixed group of degree less than or equal to n. The emphasis is on linear groups, especially compact real and p-adic…
The group theoretical description of the three-particle problem provides successful techniques for the solution of different questions. We present here a review of this approach.
This paper introduces the idea of pseudo-group. Applications of pseudo-groups in Group Theory and Symmetry Breaking in Particle Physics and Cosmology are considered.
The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…
This article is devoted to the tactical game theoretical interpretation of dialectics. Dialectical games are considered as abstractly as well as models of the internal dialogue and reflection. The models related to the representation theory…
Much has been written on reciprocity laws in number theory and their connections with group representations. In this paper we explore more on these connections. We prove a "reciprocity Law" for certain specific representations of semidirect…
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants…
The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…
In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
In this note we, first, recall that the sets of all representatives of some special ordinary residue classes become $\left( m,n\right) $-rings. Second, we introduce a possible $p$-adic analog of the residue class modulo a $p$-adic integer.…
The Whitehead asphericity problem, regarded as a problem of combinatorial group theory, asks whether any subpresentation of an aspherical group presentation is also aspherical. This is a long standing open problem which has attracted a lot…