Related papers: Representations of simple Jordan superalgebras
We compare a number of different definitions of structure algebras and TKK constructions for Jordan (super)algebras appearing in the literature. We demonstrate that, for unital superalgebras, all the definitions of the structure algebra and…
All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.
It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that…
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…
The paper is devoted to the description of the varieties of complex 5-dimensional nilpotent Jordan superalgebras. We find all representatives for the isomorphism classes, using the Jordan normal form, results of simultaneous matrix…
We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Cherednik algebras associated to the general and special…
This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.
We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.
We classify the finite dimensional irreducible representations of rectangular finite $W$-algebras, i.e., the finite $W$-algebras $U(\mathfrak{g}, e)$ where $\mathfrak{g}$ is a symplectic or orthogonal Lie algebra and $e \in \mathfrak{g}$ is…
In the article we study the simple unital communitative three-dimensional algebras over an algebraically closed field of characteristic not equal to 2. It is proved that every simple unital communitative three-dimensional algebra of…
A representation of finite-dimensional probabilistic models in terms of formally real Jordan algebras is obtained, in a strikingly easy way, from simple assumptions. This provides a framework in which real, complex and quaternionic quantum…
Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.
We compute and provide a detailed description on the Jordan constants of the multiplicative subgroup of quaternion algebras over number fields of small degree. As an application, we determine the Jordan constants of the multiplicative…
Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…
Recently, the classical Freudenthal Magic Square has been extended over fields of characteristic 3 with two more rows and columns filled with (mostly simple) Lie superalgebras specific of this characteristic. This Supermagic Square will be…
In positive characteristic the Jordan plane covers a finite-dimensional Nichols algebra that was described by Cibils, Lauve and Witherspoon and we call the restricted Jordan plane. In this paper the characteristic is odd. The defining…
We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.
We give a geometric classification of 4-dimensional superalgebras over an algebraic closed field.