12 citations · 86 across the 29 of their papers we have counts for
8 papers · 1 filter
Simple modules over the 4-dimensional Sklyanin Algebras at points of finite order
S. Paul Smith
In 1982 E.K. Sklyanin defined a family of graded algebras , depending on an elliptic curve and a point that is not 4-torsion. The present paper is concerned wi…
New Artin-Schelter regular and Calabi-Yau algebras via normal extensions
Alex Chirvasitu, Ryo Kanda, S. Paul Smith
We introduce a new method to construct 4-dimensional Artin-Schelter regular algebras as normal extensions of (not necessarily noetherian) 3-dimensional ones. The method produces la…
Some algebras having relations like those for the 4-dimensional Sklyanin algebras
A. Chirvasitu, S. Paul Smith
The 4-dimensional Sklyanin algebras are a well-studied 2-parameter family of non-commutative graded algebras, often denoted A(E,tau), that depend on a quartic elliptic curve E in P…
Exotic Elliptic Algebras of dimension 4 (with an Appendix by Derek Tomlin)
Alex Chirvasitu, S. Paul Smith
This is a continuation of our previous paper 1502.01744. We examine a class of non-commutative algebras A that depend on an elliptic curve and a translation automorphism of it. The…
Non-commutative quadric surfaces
S. Paul Smith, M. Van den Bergh
The 4-dimensional Sklyanin algebra is the homogeneous coordinate ring of a noncommutative analogue of projective 3-space. The degree-two component of the algebra contains a 2-dimen…
The Grothendieck Group of a Quantum Projective Space Bundle
I. Mori, S. Paul Smith
We compute the Grothendieck group K_0 of non-commutative analogues of quantum projective space bundles. Our results specialize to give the Grothendieck groups of non-commutative an…