Azumaya loci and discriminant ideals of PI algebras

@article{Brown2017AzumayaLA,
  title={Azumaya loci and discriminant ideals of PI algebras},
  author={Kenneth A. Brown and Milen Yakimov},
  journal={Advances in Mathematics},
  year={2017}
}
View PDF on arXiv
33 Citations
Background Citations
13
Methods Citations
5
Results Citations
2

33 Citations

Poisson geometry of PI 3-dimensional Sklyanin algebras.

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

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

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

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

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

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

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

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

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

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.

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

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…

Rigidity of quadratic Poisson tori

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

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

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…

Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras

Lectures on Algebraic Quantum Groups

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

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

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

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…