2 Edward Frenkel And
نویسنده
چکیده
We define the Hopf algebra structure on the Grothendieck group of finitedimensional polynomial representations of Uq ĝlN in the limit N → ∞. The resulting Hopf algebra Rep Uq ĝl∞ is a tensor product of its Hopf subalgebras Repa Uqĝl∞, a ∈ C/q. When q is generic (resp., q is a primitive root of unity of order l), we construct an isomorphism between the Hopf algebra Repa Uq ĝl∞ and the algebra of regular funtions on the prounipotent proalgebraic group S̃L − ∞ (resp., G̃L − l ). When q is a root of unity, this isomorphism identifies the Hopf subalgebra of Repa Uq ĝl∞ spanned by the modules obtained by pull-back with respect to the Frobenius homomorphism, with the algebra of functions on the center of G̃L − l . In addition, we construct a natural action of the Hall algebra associated to the infinite linear quiver (resp., the cyclic quiver with l vertices) on Repa Uq ĝl∞ and describe the span of tensor products of evaluation representations taken at fixed points as a module over this Hall algebra.
منابع مشابه
A Brief Introduction to Infinity by Edward Frenkel
I recently discussed these questions with Edward Frenkel, Berkeley mathematics professor and author of “Love and Math: The Heart of Hidden Reality.” “We have many ways to connect to infinity: through art, through poetry, through love,” explained Dr. Frenkel. “But mathematics gives us perhaps the most cerebral and logical way to connect to the infinite. So in this day and age, when we tend to pu...
متن کاملThe comparison effects of eight weeks spark and frenkel exercises on static and dynamic balance in the blinds
Introduction: One of the most important human senses is vision, which its loss is causing many primary and secondary complications for physical and psychological health such as difficulties in static and dynamic balance. This study aimed to compare the effect of 8 weeks of Spark and Frenkel exercises training on the static and dynamic balance in blind people. ...
متن کامل2 2 Fe b 20 01 Jet Schemes of Locally Complete Intersection Canonical Singularities
Let X be a variety defined over an algebraically closed field k of characteristic zero. The mth jet scheme Xm of X is a scheme whose closed points over x ∈ X are morphisms OX,x −→ k[t]/(t ). When X is a smooth variety, this is an affine bundle over X, of dimension (n + 1) dim X. The space of arcs X∞ of X is the projective limit X∞ = proj limmXm. Our main result is a proof of the following theor...
متن کاملA pr 2 00 1 Jet Schemes of Locally Complete Intersection Canonical
Let X be a variety defined over an algebraically closed field k of characteristic zero. The mth jet scheme Xm of X is a scheme whose closed points over x ∈ X are morphisms OX,x −→ k[t]/(t ). When X is a smooth variety, this is an affine bundle over X, of dimension (m + 1) dim X. The space of arcs X∞ of X is the projective limit X∞ = proj limmXm. Our main result is a proof of the following theor...
متن کاملA ug 2 00 0 Jet Schemes of L . C . I . Canonical Singularities
Let X be a variety defined over an algebraically closed field k of characteristic zero. The mth jet scheme Xm of X is a scheme whose closed points over x ∈ X are morphisms OX,x −→ k[t]/(t ). When X is a smooth variety, this is an affine bundle over X, of dimension (n + 1) dim X. The space of arcs X∞ of X is the projective limit X∞ = proj limmXm. Our main result is a proof of the following theor...
متن کامل