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Representations of hyper loop algebras and equivariant map algebras

Grant number: 11/22322-4
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): April 01, 2012
Effective date (End): June 30, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Adriano Adrega de Moura
Grantee:Angelo Calil Bianchi
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The project aims at studying some aspects of the representation theory of certain algebras which can be regarded as generalizations of the concept of affine Kac-Moody algebras. It is split in two parts.The first part is a natural continuation of the studies which made part of the beneficiary s Ph.D. thesis on finite-dimensional representations of twisted hyper loop algebras. In this direction, we intend to extend to the hyperalgebra context in positive characteristic several results obtained recently in characteristic zero (where the language of hyperalgebras reduces to that of Lie algebras). Examples of such results are the theories of global Weyl modules and Demazure modules.The second and more relevant part of the project will be co-supervised by Professor Vyacheslav Futorny from IME-USP. The subject of study here is the infinite-dimensional representation theory of equivariant map algebras. We will investigate questions similar to those investigated by Professor Futorny in the context of affine Kac-Moody algebras such as the theory of Verma type modules and their free field realizations using the theory of vertex algebras.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BIANCHI, ANGELO; MACEDO, TIAGO; MOURA, ADRIANO. ON DEMAZURE AND LOCAL WEYL MODULES FOR AFFINE HYPERALGEBRAS. PACIFIC JOURNAL OF MATHEMATICS, v. 274, n. 2, p. 257-303, . (11/22322-4, 09/05887-8)
BENNETT, MATTHEW; BIANCHI, ANGELO. Tilting Modules in Truncated Categories. Symmetry Integrability and Geometry-Methods and Applications, v. 10, . (11/22322-4, 12/06923-0)
BIANCHI, ANGELO; CHARI, VYJAYANTHI; FOURIER, GHISLAIN; MOURA, ADRIANO. On Multigraded Generalizations of Kirillov-Reshetikhin Modules. ALGEBRAS AND REPRESENTATION THEORY, v. 17, n. 2, p. 519-538, . (11/22322-4)

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