We prove that quantized multiplicative quiver varieties, quantum character varieties, and
Kauffman bracket skein algebras each define sheaves of Azumaya algebras over the …

We prove that, under mild assumptions, for all positive integers ℓ, the zero set of the
discriminant ideal D ℓ (R/Z (R), tr) of a prime affine polynomial identity (PI) algebra R …

arXiv:2309.05511v1 [math.RA] 11 Sep 2023 Page 1 arXiv:2309.05511v1 [math.RA] 11 Sep
2023 POISSON VALUATIONS HONGDI HUANG, XIN TANG, XINGTING WANG, AND JAMES …

We introduce the reflexive hull discriminant as a tool to study noncommutative algebras that
are finitely generated, but not necessarily free, over their centers. As an example, we …

We develop a Poisson geometric framework for studying the representation theory of all
contragredient quantum super groups at roots of unity. This is done in a uniform fashion by …

We study the Zariski cancellation problem for Poisson algebras asking whether A [t]≅ B [t]
implies A≅ B when A and B are Poisson algebras. We resolve this affirmatively in the cases …

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 …

When $ A=\Bbbk [x_1,\ldots, x_n] $ and $ G $ is a small subgroup of $\operatorname {GL} _n
(\Bbbk) $, Auslander's Theorem says that the skew group algebra $ A\# G $ is isomorphic to …

The algebras Q n, k (E, τ) introduced by Feigin and Odesskii as generalizations of the 4-
dimensional Sklyanin algebras form a family of quadratic algebras parametrized by coprime …

The two main approaches to the study of irreducible representations of orders (via traces
and Poisson orders) have so far been applied in a completely independent fashion. We …