## 33 Citations

### Poisson geometry of PI 3-dimensional Sklyanin algebras.

- Mathematics
- 2018

We give the 3-dimensional Sklyanin algebras $S$ that are module-finite over their center $Z$ the structure of a Poisson $Z$-order (in the sense of Brown-Gordon). We show that the induced Poisson…

### Representations of Quantum Nilpotent Algebras at Roots of Unity, and Their Completely Prime Quotients

- Mathematics
- 2019

This thesis studies algebras contained in a large class of iterated Ore extensions, as well as their quotient algebras by completely prime ideals, and develops methods for computing their…

### The Poisson geometry of the 3-dimensional Sklyanin algebras

- Mathematics
- 2017

We give the 3-dimensional Sklyanin algebras $S$ that are module-finite over their center $Z$ the structure of a Poisson $Z$-order (in the sense of Brown-Gordon). We show that the induced Poisson…

### Poisson geometry and representations of PI 4-dimensional Sklyanin algebras

- MathematicsSelecta Mathematica
- 2021

Take S to be a 4-dimensional Sklyanin (elliptic) algebra that is module-finite over its center Z ; thus, S is PI. Our first result is the construction of a Poisson Z -order structure on S such that…

### Poisson geometry and representations of PI 4-dimensional Sklyanin algebras

- MathematicsSelecta Mathematica
- 2021

Take S to be a 4-dimensional Sklyanin (elliptic) algebra that is module-finite over its center Z; thus, S is PI. Our first result is the construction of a Poisson Z-order structure on S such that the…

### Root of unity quantum cluster algebras and discriminants

- Mathematics
- 2020

We describe a connection between the subjects of cluster algebras and discriminants. For this, we define the notion of root of unity quantum cluster algebras and prove that they are polynomial…

### Poisson Dixmier-Moeglin equivalence from a topological point of view

- MathematicsIsrael Journal of Mathematics
- 2021

A complex affine Poisson algebra A is said to satisfy the Poisson Dixmier-Moeglin equivalence if the Poisson cores of maximal ideals of A are precisely those Poisson prime ideals that are locally…

### PI Degree and Irreducible Representations of Quantum Determinantal Rings and their Associated Quantum Schubert Varieties

- Mathematics
- 2022

We study quantum determinantal rings at roots of unity and calculate the PI degree using results in [LR08] and [Hay08] to reduce the problem to ﬁnding properties of their associated matrices. These…

### Poisson geometry of PI three‐dimensional Sklyanin algebras

- MathematicsProceedings of the London Mathematical Society
- 2018

We give the three‐dimensional Sklyanin algebras S that are module‐finite over their center Z , the structure of a Poisson Z ‐order (in the sense of Brown–Gordon). We show that the induced Poisson…

### A Note on Generic Clifford Algebras of Binary Cubic Forms

- MathematicsAlgebras and Representation Theory
- 2019

We study the representation theoretic results of the binary cubic generic Clifford algebra C $\mathcal C$ , which is an Artin-Schelter regular algebra of global dimension five. In particular, we show…

## References

SHOWING 1-10 OF 37 REFERENCES

### Poisson geometry of PI 3-dimensional Sklyanin algebras.

- Mathematics
- 2018

We give the 3-dimensional Sklyanin algebras $S$ that are module-finite over their center $Z$ the structure of a Poisson $Z$-order (in the sense of Brown-Gordon). We show that the induced Poisson…

### The Poisson geometry of the 3-dimensional Sklyanin algebras

- Mathematics
- 2017

### Rigidity of quadratic Poisson tori

- Mathematics
- 2016

We prove a rigidity theorem for the Poisson automorphisms of the function fields of tori with quadratic Poisson structures over fields of characteristic 0. It gives an effective method for…

### Homological Properties of (Graded) Noetherian PI Rings

- Mathematics
- 1994

Abstract Let R be a connected, graded, Noetherian PI ring. If injdim( R ) = n R is Auslander-Gorenstein and Cohen-Macaulay, with Gelfand-Kirillov dimension equal to n . If gldim( R ) = n R is a…

### Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism

- Mathematics
- 2000

Abstract.To any finite group Γ⊂Sp(V) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ of the algebra ℂ[V]#Γ, smash product of Γ with the polynomial…

### Lectures on Algebraic Quantum Groups

- Mathematics
- 2002

This book consists of an expanded set of lectures on algebraic aspects of quantum groups, concentrating particularly on quantized coordinate rings of algebraic groups and spaces and on quantized…

### Quantum Groups

- Mathematics
- 1993

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions…

### Quantized Weyl algebras at roots of unity

- Mathematics
- 2016

We classify the centers of the quantized Weyl algebras that are polynomial identity algebras and derive explicit formulas for the discriminants of these algebras over a general class of polynomial…

### Localization in Non-Commutative Noetherian Rings

- MathematicsCanadian Journal of Mathematics
- 1976

To construct a well behaved localization of a noetherian ring R at a semiprime ideal S, it seems necessary to assume that the set (S) of modulo S regular elements satisfies the Ore condition ; and it…