Related papers: Quiver algebras, weighted projective lines, and th…
We provide a geometric-combinatorial model for the category of coherent sheaves on the weighted projective line of type (2,2,n) via a cylindrical surface with n marked points on each of its upper and lower boundaries, equipped with an order…
In this article, we deal with the structure of the spherical Hall algebra of coherent sheaves with parabolic structures on a smooth projective curve of arbitrary genus. We provide a shuffle-like presentation of the vector bundle part and…
We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type C. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we…
We study local algebras, which are structures similar to $\mathbb{Z}$-graded algebras concentrated in degrees $-1,0,1$, but without a product defined for pairs of elements at the same degree $\pm1$. To any triple consisting of a Kac-Moody…
We consider the subalgebras of split real, non-twisted affine Kac-Moody Lie algebras that are fixed by the Chevalley involution. These infinite-dimensional Lie algebras are not of Kac-Moody type and admit finite-dimensional unfaithful…
We study the cohomological Hall algebra Y of a lagrangian substack of the moduli stack of representations of the preprojective algebra of an arbitrary quiver Q, and their actions on the cohomology of Nakajima quiver varieties. We prove that…
We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac-Moody algebra. As byproducts, we obtain a geometric realization of Lusztig's canonical bases of these representations as well…
We prove that the weight multiplicities of the integrable irreducible highest weight module over the Kac-Moody algebra associated to a quiver are equal to the root multiplicities of the Kac-Moody algebra associated to some enlarged quiver.…
We study representations of the Loop Kac-Moody Lie algebra g \otimes A, where g is any Kac-Moody algebra and A is a ring of Laurent polynomials in n commuting variables. In particular, we study representations with finite dimensional weight…
Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call…
We review the definition of quiver varieties and their relation to representation theory of Kac-Moody Lie algebras. Target readers are ring and representation theorists. We emphasize important roles of first extension groups of the…
Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular the presentation of the coordinate algebra of the…
Inspired by Morse theory, we introduce a topological stack Broken, which we refer to as the moduli stack of broken lines. We show that Broken can be presented as a Lie groupoid with corners and provide a combinatorial description of sheaves…
We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves…
Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.
This paper classifies irreducible, integrable highest weight modules for "current Kac-Moody Algebras" with finite dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many…
The $\imath$Hall algebra of the projective line is by definition the twisted semi-derived Ringel-Hall algebra of the category of $1$-periodic complexes of coherent sheaves on the projective line. This $\imath$Hall algebra is shown to…
We present a largely self contained account on the K-theory of a weighted smooth projective curve over an algebraically closed field. In particular, we discuss the weighted version of divisor theory, Euler form, and Riemann-Roch theorem.…
In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family…
In this thesis, we study counts of quiver representations over finite rings of truncated power series. We prove a plethystic formula relating counts of quiver representations over these rings and counts of jets on fibres of quiver moment…