Artin-Schelter regular algebras from dual reflections groups

Let A be an Artin-Schelter regular algebra that is graded by a finite group G,
and let Ae denote the identity component of A. We call G a dual reflection group
for A when under the action of the Hopf algebra H = (kG)
∗
, the dual of the group
algebra, the ring of invariants, AH ∼= Ae, is also Artin-Schelter regular. We view the
property that both A and AH are Artin-Schelter regular as a generalization of the
Shephard-Todd-Chevalley Theorem on the invariants of a commutative polynomial
ring under the action of a reflection group. Using necessary conditions for such a
pair (A, G) to exist, for certain groups G of order 16 we have constructed several
interesting 4-dimensional Artin-Schelter algebras A and studied their geometric and
algebraic properties, and the relationship between these properties.

Please report video problems to itsupport@slmath.org.

See more of our Streaming videos on our main VMath Videos page.