The homological determinant of quatum groups of type A

Skew Calabi-Yau Algebras and Homological Identities

A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A # H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A and a finite-dimensional Hopf algebra H that acts on it; (ii) how the Nakayama automorphism of a graded twist of A is related to the Nakayama automorphism of A; and (iii) that Nakayama automorphism of…

On quantum groups associated to non-Noetherian regular algebras of dimension 2

We investigate homological and ring-theoretic properties of universal quantum linear groups that coact on Artin-Schelter regular algebras A(n) of global dimension 2, especially with central homological codeterminant (or central quantum determinant). As classified by Zhang, the algebras A(n) are connected \N-graded algebras that are finitely generated by n indeterminants of degree 1, subject to one quadratic relation. In the case when the homological codeterminant of the coaction is trivial, we show that the quantum group of interest, defined independently by Manin and by Dubois-Violette and La…

McKay Correspondence for semisimple Hopf actions on regular graded algebras, I

In establishing a more general version of the McKay correspondence, we prove Auslander's theorem for actions of semisimple Hopf algebras H on noncommutative Artin-Schelter regular algebras A of global dimension two, where A is a graded H-module algebra, and the Hopf action on A is inner faithful with trivial homological determinant. We also show that each fixed ring A^H under such an action arises an analogue of a coordinate ring of a Kleinian singularity.

关于Kadar-Yu代数的半单性标准及非半单表示理论的准则

On semisimplicity criteria and non-semisimple representation theory for the Kadar-Yu algebras

本文研究Kadar-Yu代数的非半单表示理论，通过广义Chebyshev型形式扩展了Temperley-Lieb代数的根单位元范式，并在Brauer代数的积分范式之间进行插值。