Gavarini, Fabio
Published in
Forum Mathematicum

In this note I fix a mistake in my previous paper [5]: namely, the result concerning the uniqueness (up to isomorphisms) of such supergroups needs a new formulation and proof. By the same occasion, I explain more in detail the existence result which comes out of the construction of Chevalley supergroups.

Gavarini, Fabio
Published in
Forum Mathematicum

I present a construction of connected affine algebraic supergroups šV associated with simple Lie superalgebras š¤ of Cartan type and with š¤-modules V. Conversely, I prove that every connected affine algebraic supergroup whose tangent Lie superalgebra is of Cartan type is necessarily isomorphic to one of the supergroups šV that I introduced. In parti...

Holdaway, Cody Sisodia, Gautam
Published in
Journal of Algebra

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A=kQ/I. Let QGrA denote the quotient of the category of graded right A-modules modulo the Serre subcategory consisting of those graded mo...

Solanki, Vinesh Sustretov, Dmitry Zilber, Boris
Published in
Annals of Pure and Applied Logic

A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field F of characteristic 0, which is shown to be uncountably categorical. An analysis of definable sets is carried out, from which it follows that this structure is a Zariski geometry of dimension 1. It is non-classical in the sense that it is not int...

Solanki, Vinesh Sustretov, Dmitry Zilber, Boris
Published in
Annals of Pure and Applied Logic

Holdaway, Cody Sisodia, Gautam
Published in
Journal of Algebra

Backelin, Erik Kremnizer, Kobi
Published in
Advances in Mathematics

We quantize parabolic flag manifolds and describe categories of quantum D-modules on them at a singular central character. We compute global sections of generators for these categories for any qāCā. For generic q we prove a singular version of BeilinsonāBernstein localization for a quantized enveloping algebra.

Burban, Igor Kalck, Martin
Published in
Advances in Mathematics

In this article, we study a triangulated category associated with a non-commutative resolution of singularities. In particular, we give a complete description of this category in the case of a curve with nodal singularities, classifying its indecomposable objects and computing its AuslanderāReiten quiver and K-group.

Craw, Alastair Velez, Alexander Quintero

This paper constructs cellular resolutions for classes of noncommutative algebras, analogous to those introduced by Bayer-Sturmfels in the commutative case. To achieve this we generalise the dimer model construction of noncommutative crepant resolutions of toric algebras in dimension three by associating a superpotential and a notion of consistency...

Rogalski, D.
Published in
Advances in Mathematics

We describe some interesting graded rings which are generated by degree-3 elements inside the Sklyanin algebra S, and prove that they have many good properties. Geometrically, these rings R correspond to blowups of the Sklyanin P 2 at 7 or fewer points. We show that the rings R are exactly those degree-3-generated subrings of S which are maximal or...