5 citations · 18 across the 12 of their papers we have counts for
14 papers
The symplectic leaves for the elliptic Poisson bracket on projective space defined by Feigin-Odesskii and Polishchuk
Alexandru Chirvasitu, Ryo Kanda, S. Paul Smith
This paper determines the symplectic leaves for a remarkable Poisson structure on discovered by Feigin and Odesskii, and, independently, by Polishchuk.…
Modular properties of elliptic algebras
Alex Chirvasitu, Ryo Kanda, S. Paul Smith
Fix a pair of relatively prime integers , and a point , where denotes the upper-half complex plane, and let ${{a\;\,b…
Elliptic R-matrices and Feigin and Odesskii's elliptic algebras
Alex Chirvasitu, Ryo Kanda, S. Paul Smith
The algebras introduced by Feigin and Odesskii as generalizations of the 4-dimensional Sklyanin algebras form a family of quadratic algebras parametrized by coprime…
Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings
Alex Chirvasitu, Ryo Kanda, S. Paul Smith
The elliptic algebras in the title are connected graded -algebras, denoted , depending on a pair of relatively prime integers , an elliptic curv…
Projective discrete modules over profinite groups
Alexandru Chirvasitu, Ryo Kanda
We show that the category of discrete modules over an infinite profinite group has no non-zero projective objects and does not satisfy Ab4*. We also prove the same types of results…
Finite quotients of powers of an elliptic curve
Alex Chirvasitu, Ryo Kanda, S. Paul Smith
Let be an elliptic curve. When the symmetric group of order acts on in the natural way, the subgroup , consisting of those -tuple…
The characteristic variety for Feigin and Odesskii's elliptic algebras
Alex Chirvasitu, Ryo Kanda, S. Paul Smith
This paper examines an algebraic variety that controls an important part of the structure and representation theory of the algebra introduced by Feigin and Odesskii.…
Feigin and Odesskii's elliptic algebras
Alex Chirvasitu, Ryo Kanda, S. Paul Smith
We study the elliptic algebras introduced by Feigin and Odesskii as a generalization of Sklyanin algebras. They form a family of quadratic algebras parametrized by c…
Flat families of point schemes for connected graded algebras
Alex Chirvasitu, Ryo Kanda
We study truncated point schemes of connected graded algebras as families over the parameter space of varying relations for the algebras, proving that the families are flat over th…
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…
Non-commutative Geometry of Homogenized Quantum
Alex Chirvasitu, S. Paul Smith, Liang Ze Wong
This paper examines the relationship between certain non-commutative analogues of projective 3-space, , and the quantized enveloping algebras .…
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…
Exotic Elliptic Algebras
Alex Chirvasitu, S. Paul Smith
This paper examines a general method for producing twists of a comodule algebra by tensoring it with a torsor then taking co-invariants. We examine the properties that pass from th…