TY - GEN
T1 - Modular properties of elliptic algebras
AU - Chirvasitu, Alex
AU - Kanda, Ryo
AU - Paul Smith, S.
N1 - Publisher Copyright: © 2024 American Mathematical Society.
PY - 2024
Y1 - 2024
N2 - Fix a pair of relatively prime integers n>k≥1, and a point (η | τ) ∈ C×H, where H denotes the upper-half complex plane, and let a b c d ∈ SL(2, Z). We show that Feigin and Odesskii’s elliptic algebras Qn,k(η|τ) have the property Qn,k formula presented∼=Qn,k(η|τ). As a consequence, given a pair (E, ξ) consisting of a complex elliptic curve E and a point ξ ∈ E, one may unambiguously define Qn,k(E, ξ):=Qn,k(η|τ) where τ ∈ H is any point such that C/Z +Zτ∼=E and η ∈ C is any point whose image in E is ξ. This justifies Feigin and Odesskii’s notation Qn,k(E, ξ) for their algebras. The algebras Qn,1(η|τ) are commonly known as Sklyanin algebras in honor of Sklyanin’s discovery of Q4,1(η|τ).
AB - Fix a pair of relatively prime integers n>k≥1, and a point (η | τ) ∈ C×H, where H denotes the upper-half complex plane, and let a b c d ∈ SL(2, Z). We show that Feigin and Odesskii’s elliptic algebras Qn,k(η|τ) have the property Qn,k formula presented∼=Qn,k(η|τ). As a consequence, given a pair (E, ξ) consisting of a complex elliptic curve E and a point ξ ∈ E, one may unambiguously define Qn,k(E, ξ):=Qn,k(η|τ) where τ ∈ H is any point such that C/Z +Zτ∼=E and η ∈ C is any point whose image in E is ξ. This justifies Feigin and Odesskii’s notation Qn,k(E, ξ) for their algebras. The algebras Qn,1(η|τ) are commonly known as Sklyanin algebras in honor of Sklyanin’s discovery of Q4,1(η|τ).
UR - https://www.scopus.com/pages/publications/85204709702
U2 - 10.1090/conm/801/16037
DO - 10.1090/conm/801/16037
M3 - Conference contribution
SN - 9781470472399
T3 - Contemporary Mathematics
SP - 73
EP - 94
BT - Recent Advances in Noncommutative Algebra and Geometry - Conference in Honor of S. Paul Smith on the Occasion of His 65th Birthday Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, 2022
A2 - Brown, K.A.
A2 - Hodges, T.J.
A2 - Vancliff, M.
A2 - Zhang, J.J.
PB - American Mathematical Society
T2 - Conference on Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, 2022, held in honor of S. Paul Smith on the occasion of his 65th Birthday
Y2 - 20 June 2022 through 24 June 2022
ER -