View abstract

Session S16 - Quantum symmetries

Friday, July 16, 14:20 ~ 14:45 UTC-3

Universal (co)acting Hopf algebras

Ana Agore

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak99ea6bc350c6f1d6b153f2d25c3dea6d').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy99ea6bc350c6f1d6b153f2d25c3dea6d = '&#97;n&#97;.&#97;g&#111;r&#101;' + '&#64;'; addy99ea6bc350c6f1d6b153f2d25c3dea6d = addy99ea6bc350c6f1d6b153f2d25c3dea6d + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text99ea6bc350c6f1d6b153f2d25c3dea6d = '&#97;n&#97;.&#97;g&#111;r&#101;' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak99ea6bc350c6f1d6b153f2d25c3dea6d').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy99ea6bc350c6f1d6b153f2d25c3dea6d + '\'>'+addy_text99ea6bc350c6f1d6b153f2d25c3dea6d+'<\/a>';

We introduce the notion of support equivalence for (co)module algebras (over Hopf algebras), which generalizes in a natural way (weak) equivalence of gradings. We show that for each equivalence class of (co)module algebra structures on a given algebra $A$, there exists a unique universal Hopf algebra $H$ together with an $H$-(co)module structure on $A$ such that any other equivalent (co)module algebra structure on $A$ factors through the action of $H$. We study support equivalence and the universal Hopf algebras mentioned above for group gradings, Hopf--Galois extensions, actions of algebraic groups and cocommutative Hopf algebras. We show how the notion of support equivalence can be used to reduce the classification problem of Hopf algebra (co)actions.

Joint work with Alexey Gordienko (M. V. Lomonosov Moscow State University, Russia) and Joost Vercruysse (Universite Libre de Bruxelles, Belgium).