相关论文: Representability of affine algebras over an arbitr…
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 present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…
Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.
We prove a new formula for the generating function of polynomials counting absolutely stable representations of quivers over finite fields. The case of irreducible representations is studied in more detail.
We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…
We give Erdmann-Nakano type theorem for the finite quiver Hecke algebras $R^{\Lambda_0}(\beta)$ of affine type $A^{(1)}_{\ell}$. Note that each finite quiver Hecke algebra lies in one parameter family, and the original Erdmann-Nakano…
We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…
We study finite dimensional representations over some Noetherian algebras over a field of characteristic zero. More precisely, we give necessary and sufficient conditions for the category of locally finite dimensional representations to be…
We study the classical and quantum $G$ extended superconformal algebras from the hamiltonian reduction of affine Lie superalgebras, with even subalgebras $G\oplus sl(2)$. At the classical level we obtain generic formulas for the Poisson…
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…
We consider the following question, concerning associative algebras R over an algebraically closed field k: When can the space of (equivalence classes of) finite dimensional irreducible representations of R be topologically embedded into a…
In this paper we prove that every irreducible representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition. We also prove that - in general - for (semi)simple…
We study the problem of existence of pushouts in the category of algebraic sets over an infinite field. This problem can be reduced to asking whether the property of being a finitely generated algebra over a field, or a Noetherian ring in…
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…
The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothendieck ring of the category of finitely generated…
We study amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group…
In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.
We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type A. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we…
We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…