Extensions of modules for twisted current algebras

Jean Auger, Michael Lau

Published 2017-04-13Version 1

Twisted current algebras are fixed point subalgebras of current algebras under a finite group action. Special cases include equivariant map algebras and twisted forms of current algebras. We compute the extensions between any pair of simple modules in the category of finite-dimensional modules over a twisted current algebra, and then use this information to determine the block decomposition of the category. We illustrate our results with an application to twisted forms of current algebras.