Fq[Mn], Fq[GLn] and Fq[Sn] as Quantized Hyperalgebras

Host Institution:

La Trobe University

Title of Seminar:

Fq[Mn],  Fq[GLn] and Fq[Sn] as Quantized Hyperalgebras

Speaker's Name:

Professor Zoran Rakić

Speaker's Institution:

University of Belgrade, Serbia

Time and Date:

Monday 21st November, 2011, 12:00 PM (AEDT)

Seminar Abstract:

The first part of the lecture is introductory. The notions of Hopf algebra, quantum group, quantum function algebra, quantum Frobenius morphism and some basic examples will be given. In the second part, we consider the quantum function algebra Fq[GLn] and study the subset Fq[GLn] of all elements of Fq[GLn]  which are Z[q, q-1]-valued when paired with Uq(gln), the unrestricted Z[q, q-1]-integral form of Uq(gln), introduced by De Concini, Kac and Procesi. In particular we obtain a presentation of it by generators and relations and a PBW-like theorem. Moreover, we give a direct proof that Fq[GLn] is a Hopf subalgebra of Fq[GLn], and that Fq[GLn]|q=1= UZ (gln*). We describe explicitly its specializations at roots of 1, say ε, and the associated quantum Frobenius (epi)morphism from Fε[GLn] to F1[GLn] = UZ (gln*). The same analysis is done for Fq[SLn] and (as key step) for Fq[Sn].

This talk is based on joint work with Fabio Gavarini, University Tor Vergata, Rome.

Seminar Convenor:

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