Realizations of BC_r-graded intersection matrix algebras with grading subalgebras of type B_r, r ≥ 3

Sandeep Bhargava and Yun Gao

Vol. 263 (2013), No. 2, 257–281

DOI: 10.2140/pjm.2013.263.257

Abstract

We study intersection matrix algebras imA^[d] that arise from affinizing a Cartan matrix A of type B_r with d arbitrary long roots in the root system Δ_Br, where r ≥ 3. We show that imA^[d] is isomorphic to the universal covering algebra of so_2r+1a,η,C,χ, where a is an associative algebra with involution η, and C is an a-module with hermitian form χ. We provide a description of all four of the components a, η, C, and χ.

Keywords

Lie algebras, intersection matrix algebras

Mathematical Subject Classification 2010

Primary: 17B65, 17B70, 17B05

Secondary: 17B67, 16W10

Milestones

Received: 22 April 2012

Revised: 28 August 2012

Accepted: 9 October 2012

Published: 31 May 2013