Hall algebras
Hall algebras and quantum groups.
Hall algebras, hereditary algebras and quantum groups.
Hall algebras of two equivalent extriangulated categories
For any positive integer , let be a linearly oriented quiver of type with vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories and , where and are the two extriangulated categories corresponding to the representation category of and the morphism category of projective representations of , respectively. As a by-product,...
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...
Harmonic analysis on quantum spheres associated with representations of and -jacobi polynomials
Hermite -polynomials and -oscillators
Higher dimensional algebra. VII: Groupoidification.
Hochschild homology and cohomology of generalized Weyl algebras
We compute Hochschild homology and cohomology of a class of generalized Weyl algebras, introduced by V. V. Bavula in St. Petersbourg Math. Journal, 4 (1) (1999), 71-90. Examples of such algebras are the n-th Weyl algebras, , primitive quotients of , and subalgebras of invariants of these algebras under finite cyclic groups of automorphisms. We answer a question of Bavula–Jordan (Trans. A.M.S., 353 (2) (2001), 769-794) concerning the generators of the group of automorphisms of a generalized Weyl...
Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of ‘quantum’ type in all but a few exceptional cases.
Homogeneous representations of Khovanov–Lauda Algebras
We construct irreducible graded representations of simply laced Khovanov–Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types has been developed previously by Peterson, Proctor and Stembridge. In particular, the Peterson–Proctor hook formula gives the dimensions of the homogeneous irreducible modules corresponding to straight shapes.
Homotopy theory of Hopf Galois extensions
We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all -Galois extensions up to homotopy equivalence in the case when is a Drinfeld-Jimbo quantum group.
How to categorify one-half of quantum 𝔤𝔩(1|2)
We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra 𝔤𝔩(1|2).