COSAM » Events » 2019 » April » DMS Linear Algebra/Algebra Seminar

DMS Linear Algebra/Algebra Seminar
Time: Apr 16, 2019 (04:00 PM)
Location: Parker Hall 354


Speaker: Yong Liu

Title: Bundled Lie algebra of type A

Abstract: On the set of all traceless square matrices over the complex numbers, we impose an equivalence relation defined by the Kronecker product. The resulting quotient space becomes an infinite dimensional (Lie) algebra (called bundled Lie algebra) with respect to the semi-tensor product and addition. These two algebraic structures are natural generalization of the usual matrix product and addition which have many applications in control theory. As a direct limit of the simple Lie algebras sl(n) of type A, this bundled Lie algebra in fact lies in the class of diagonal embedding Lie algebras. We give answers to some of the basic questions in the aspect of (Lie) algebras, such as basis, root space decomposition and standard representations.

Last updated: 04/16/2019