Some studies in Matrix Theory and applications to generalised clifford algebras and representations of Lie groups

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Some studies in Matrix Theory and applications to generalised clifford algebras and representations of Lie groups

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Title: Some studies in Matrix Theory and applications to generalised clifford algebras and representations of Lie groups
Author: Madivanane, S.
Advisor: Santhanam, T. S.
Degree: Ph.D
Main Subjects: Physics
Institution: University of Madras
Year: 1988
Pages: iii; 95p.
Abstract: Some aspects of Matrix theory and its applications are dealt with in this thesis. "For two matrices A and B of order n x n which satisfy the characteristic equation( x^n) - 1 = 0 , it has been shown that the transformation matrix T (AB) satisfying the relation AT (AB) = T (AB) B, becomes involutional". Clifford and generalised Clifford algebras and their representations, are discussed in this thesis. The theorem on involutional matrices, and Lomont's generalisation, Quantum mechanics of a n-level system, its relationship to Kuryshkin's q-algebras, Finite fourier transform, formation of Hamiltonian of a trunkated harmonic oscillator, indecompasble representations of some Lie algebras,... are some of the concepts discussed and explained in this thesis.
URI: http://hdl.handle.net/123456789/57

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