Related papers: Representation theorems for extended contact algeb…
The purpose of this paper is to study representations and $T$*-extensions of hom-Jordan-Lie algebras. In particular, adjoint representations, trivial representations, deformations and many properties of $T$*-extensions of hom-Jordan-Lie…
Importance of theorem dedicated to isomorphisms consist in statement that they allow to identify different mathematical objects which have something common from the point of view of certain model. This paper considers morphisms of \Ts…
Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We…
This paper develops the technique of constructing Lax representations for PDEs via non-central extensions of their contact symmetry algebras. We show that the method is applicable to the Lax representations with non-removable spectral…
In this paper we generalize the comparison theorem of Hecht and Taylor to arbitrary parabolic subalgebras of a complex reductive Lie algebra and then apply our generalized comparison theorem to obtain results about the geometric realization…
The First and Second Representation Theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the…
We study the question of when geometric extension algebras are polynomial quasihereditary. Our main theorem is that under certain assumptions, a geometric extension algebra is polynomial quasihereditary if and only if it arises from an even…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
We give a characterization of subsets of effect algebras, that can be embedded into a range of an observable. To give this characterization, we introduce a new notion of {\em compatibility support mappings.}
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.
In this paper, we introduce the notion of representation of Bol algebra. We prove an analogue of the classical Engel's theorem and the ex- tension of Ado-Iwasawa theorem for Bol Algebras. We study the category of representations of Bol…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a field $k(\!(G)\!)$ of generalised power series, exploiting our…
In this work, I develop a new view of presentation theory for C*-algebras, both unital and non-unital, heavily grounded in classical notions from algebra. In particular, I introduce Tietze transformations for these presentations, which lead…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation…