Exotic elliptic algebras

q-deformed W-algebras and elliptic algebras

The elliptic algebra Aq,p(ŝl(N)c) at the critical level c = −N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the WN algebra, are constructed. The operators t(z) also close an exchange algebra when (−p1/2)NM = q−c−N for M ∈ Z. It becomes Abelian when in addition p = qNh where h is a non-zero integer. The Poisson structures...

From the elliptic regulator to exotic relations

In this paper we prove an identity between the elliptic regulators of some 2-isogenous elliptic curves. This allow us to prove a new exotic relation for the elliptic curve 20A of Cremona’s tables. Also we prove the (conjectured) exotic relation for the curve 20B given by Bloch and Grayson in [3].

Elliptic curves and C*-algebras

We use C-algebras in the context of modular curves and holomorphic 1-forms. We focus on the “leaf space” X and C-algebra C(X) of the Weil 1-form ωN on the modular curve X0(N). It is proved that K0(C (X)) is isomorphic to a stationary dimension group of rank 4g − 3. An application of this result to Hilbert’s 12th problem is discussed.

Deformed WN algebras from elliptic sl(N) algebras

We extend to the sl(N) case the results that we previously obtained on the construction of Wq,p algebras from the elliptic algebra Aq,p(ŝl(2)c). The elliptic algebra Aq,p(ŝl(N)c) at the critical level c = −N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(N −1)/2 integers, defining q-deformations of the WN algebra, are constructed. The op...

Elliptic Genus and Kac-Moody Algebras