Vol. 263, No. 2, 2013

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Realizations of BCr-graded intersection matrix algebras with grading subalgebras of type Br, r 3

Sandeep Bhargava and Yun Gao

Vol. 263 (2013), No. 2, 257–281

We study intersection matrix algebras im(A[d]) that arise from affinizing a Cartan matrix A of type Br with d arbitrary long roots in the root system ΔBr, where r 3. We show that im(A[d]) is isomorphic to the universal covering algebra of so2r+1(a,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.

Lie algebras, intersection matrix algebras
Mathematical Subject Classification 2010
Primary: 17B65, 17B70, 17B05
Secondary: 17B67, 16W10
Received: 22 April 2012
Revised: 28 August 2012
Accepted: 9 October 2012
Published: 31 May 2013
Sandeep Bhargava
Mathematics Department, School of Liberal Arts and Sciences
Humber Institute of Technology and Advanced Learning
205 Humber College Boulevard
Toronto, ON  M9W 5L7
Yun Gao
Department of Mathematics and Statistics
York University
4700 Keele Street
Toronto, ON  M3J 1P3