Related papers: Monk Algebras and Representability
We introduce the notion of a generalized representation of a Jordan algebra with unit. The greneralized representation has the following properties: (1) Usual representations and Jacobson representations correspond to special cases of…
Let $k$ be a nonperfect separably closed field. Let $G$ be a connected reductive algebraic group defined over $k$. We study rationality problems for Serre's notion of complete reducibility of subgroups of $G$. In particular, we present a…
We provide a unified approach, via deformations of incidence algebras, to several important types of representations with finiteness conditions, as well as the combinatorial algebras which produce them. We show that over finite dimensional…
The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…
The problem of classifying all short multiplets of superconformal algebras still seems to be an open question. A generic short multiplet is non-unitary, which nevertheless is of interest in various contexts. Even if one is interested in…
Let $\pi$ be an irreducible unitary representation of a finitely generated nonabelian free group $\Gamma$; suppose $\pi$ is weakly contained in the regular representation. In 2001 the first and third authors conjectured that such a…
Let k be a field of characteristic p>0, and G be a finite group. The first result of this paper is an explicit formula for the determinant of the Cartan matrix of the Mackey algebra mu_k(G) of G over k. The second one is a formula for the…
In the present paper, a class of new simple modules over the $N=1$ Ramond algebra are constructed, which are induced from simple modules over some finite dimensional solvable Lie superalgebras. These new modules are simple restricted…
We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irreducible representations of dimension at most n for a simple…
It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $ M_{ q,p}(2) $ ( the coordinate ring of $ GL_{q,p}(2) $) exist only when both q and p are roots of unity. In this case th e space of states…
We classify irreducible SL(2,K)-modules of low Morley rank (at most 4.rk(K)) as a first step towards a more general conjecture.
Let $A$ be a commutative unital $\mathbb{R}$-algebra and let $\rho$ be a seminorm on $A$ which satisfies $\rho(ab)\leq\rho(a)\rho(b)$. We apply T. Jacobi's representation theorem to determine the closure of a $\sum A^{2d}$-module $S$ of $A$…
Let X be a locally compact space, and let A and B be Co(X)-algebras. We define the notion of an asymptotic Co(X)-morphism from A to B and construct representable E-theory groups RE(X;A,B). These are the universal groups on the category of…
Assume $A$ is weakly symmetric, indecomposable, with radical cube zero and radical square non-zero. We show that such algebra of wild representation type does not have a non-projective module $M$ whose ext algebra is finite-dimensional.…
Hilbert's 14th Problem asks the following question. Given a linear representation $ \beta: G \to \operatorname{GL}(\mathbf{V}) $ of a linear algebraic group over a field $ k $ is the ring $ S_{k}(\mathbf{V}^{\ast}) $ a finitely generated $…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
In this short note we show that every connected reductive simply-connected algebraic group of rank $>1$ over the complex numbers has infinitely many pairs of irreducible representations which are not related by an automorphism of the…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
We consider applications of a finitary version of the Affine Representability theorem, which follows from recent work of Belov-Kanel, Rowen, and Vishne. Using this result we are able to show that when given a finite set of polynomial…
A theorem of Y. Berest, P. Etingof and V. Ginzburg states that finite dimensional irreducible representations of a type A rational Cherednik algebra are classified by one rational number m/n. Every such representation is a representation of…